Nancy Fung

Slope and Direct Variation

Slide Duration:

Section 1: Variables and Algebraic Expressions
Numerical Expressions

13m 41s

Intro
0:00
What You'll Learn and Why
0:08
Topics Overview
0:09
Vocabulary
0:22
Order of Operations
0:26
Numerical Expression
1:03
Simplify
1:27
Simplifying an Expression
1:44
Example 1: Simplify the Expression
1:45
Simplifying an Expression
3:26
Example 2: Simplify the Expression
3:27
Using an Expression to Solve a Problem
4:29
Example 3: Babysitting
4:33
Using an Expression to Solve a Problem
6:14
Example 4: Shopping
6:17
Extra Example 1: Simplify the Expression
7:35
Extra Example 2: Simplify the Expression
8:55
Extra Example 3: Finding Total Cost
10:02
Extra Example 4: Finding Total Cost
11:44
Algebraic Expressions

9m 11s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Variable
0:19
Algebraic Expression
0:30
Evaluate
0:51
Modeling an Algebraic Expression
1:16
Model the Expression 2x + 4
1:17
Evaluating an Algebraic Expression
1:47
Evaluate 3x - 7 for x = 8.2
1:48
Evaluating an Algebraic Expression
2:45
Evaluate (3.7 + x) ÷ 2 for x = 9.6
2:46
Using a Table to Evaluate an Expression
4:10
Example: Pairs of Shoes
4:13
Extra Example 1: Evaluate the Expression
5:46
Extra Example 2: Evaluate the Expression
6:06
Extra Example 3: Perimeter of a Rectangle
6:46
Extra Example 4: Finding Income
7:40
Writing Expressions

8m 24s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
0:26
Subtraction
1:04
Multiplication
2:06
Division
2:31
Translating Words to Expressions
3:02
Example: 9 Less than Twice a Number
3:08
Writing an Algebraic Expression
3:58
Example: Cost of Bowling
4:07
Extra Example 1: Writing Expressions
5:14
Extra Example 2: Writing Expressions
6:06
Extra Example 3: Writing Expressions
7:11
Extra Example 4: Writing Expressions
7:58
Estimating for Reasonableness

10m 20s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
Compatible Numbers
0:17
Estimating by Rounding
1:08
Estimate 36 + 6 + 58
1:30
Estimate 94 - 35 - 42
2:29
Estimating with Compatible Numbers
3:02
Estimate 297 ÷ 17
3:17
Estimate 9 Times 38
3:39
Estimating for Reasonableness
4:13
Example: Total Cost of the Items
4:15
Extra Example 1: Estimating with Compatible Numbers
6:02
Extra Example 2: Estimating by Rounding
7:05
Extra Example 3: Estimating for Reasonableness
7:27
Extra Example 4: Estimating for Reasonableness
9:15
Properties of Numbers

12m 1s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:16
0:21
1:46
Vocabulary Cont.
3:08
3:09
Recognizing Properties
3:55
Examples: Which Property is Illustrated?
3:58
Using Properties of Numbers
5:07
Using Mental Math to Find the Total Cost
5:18
Using Properties of Numbers
6:29
Using Mental Math to Simplify
6:30
Extra Example 1: Using Properties of Numbers
8:29
Extra Example 2: Using Properties of Numbers
9:06
Extra Example 3: Using Properties of Numbers
10:02
Extra Example 4: Using Properties of Numbers
10:32
Distributive Property

9m 40s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:15
Distributive Property
0:16
Using the Distributive Property
1:32
Example: 8 ( 9 + 11 )
1:35
Using the Distributive Property
2:58
Example: 7 ( 12 - h )
2:59
Example: ( m + 2 ) 5
3:20
Distributive Property in Mental Math
3:34
Example: Finding Total Cost
3:38
Extra Example 1: Summer Job
4:55
Extra Example 2: Total Cost
6:03
Extra Example 3: Fundraiser
7:36
Extra Example 4: Tomato Plants
8:24
Section 2: Integers and Exponents
Integers and Absolute Value

11m 35s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:10
Vocabulary
0:21
Opposites
0:27
Integers
1:03
Absolute Value
1:23
Vocabulary
2:21
Number Line
2:23
Finding Absolute Value
2:35
Example: Absolute Value
2:36
More Examples
4:05
Example: Absolute Value of 5
4:06
Example: Absolute Value of Negative 2
4:15
Comparing Integers
4:29
Boiling Points of Elements
4:34
Comparing Integer Examples
6:00
Example 1: Comparing Integers
6:04
Example 2: Comparing Integers
6:17
Example 3: Comparing Integers
6:30
Comparing Integer Examples
6:49
Comparing Temperature
6:53
Extra Example 1: Simplify Absolute Value
8:13
Extra Example 2: Simplify Absolute Value
9:01
Extra Example 3: Simplify Absolute Value
9:29
Extra Example 4: Simplify Absolute Value
10:49

10m 20s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:26
Integers
0:30
0:55
Example : -3 + -7
1:01
Example : +11 + 8
1:06
Example : 2 + (+6)
1:21
1:43
Example: -3 + -7
1:48
Example: -21 + -3
2:05
Example: -11 + (-4)
2:41
3:01
Using a Number Line: -8 + 10
3:52
Using a Number Line: 4 + (-6)
4:36
5:39
Using Absolute Value: -18 + 7
5:48
6:33
7:23
Extra Example 3: Money Problem
8:46
Extra Example 4: Measurement Problem
9:15
Subtracting Integers

12m 1s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:21
Integers
0:25
Opposites
0:47
Rules for Multiplying Signs
1:18
Using a Number Line
2:00
Example: 2 - 5
2:25
Other Examples
2:52
Using Number Line: 10 - (-13)
3:02
Rewriting Absolute Value
4:51
Extra Example 1: Subtracting Integers
5:48
Extra Example 2: Temperature
7:26
Extra Example 3: Depth
8:51
Extra Example 4: Change in Yards
11:09
Multiplying Integers

14m 28s

Intro
0:00
What You'll Learn and Why
0:05
Topics Overview
0:06
Vocabulary
0:43
Integers
0:47
Opposites
1:03
1:41
Example 1: Using a Number Line
1:43
More Examples
3:28
Example 2: Using a Number Line
3:30
Using a Number Line
4:45
Example 3: Using a Number Line
4:46
Example 4: Using a Number Line
5:59
7:20
Arithmetic
7:35
Algebra
8:00
Rules for Multiplying Different Signs Integers
8:17
Arithmetic
8:29
Algebra
8:58
Multiplying Integer Examples
9:20
Examples of Multiplying Integers
9:21
Using Multiplication of Integers to Solve a Problem
10:07
Elevation
10:12
Temperature
11:21
Determine the Sign of the Product
12:19
Example 5: Determine the Sign
12:20
Example 6: Determine the Sign
12:50
Extra Example 1: Product of Three Negative Numbers
13:07
Extra Example 2: Product of Four Negative Numbers
13:45
Extra Example 3: Product of Five Negative Numbers
13:58
Extra Example 4: Product of 103 Negative Numbers
14:13
Dividing Integers

20m 18s

Intro
0:00
What You'll Learn and Why
0:06
Topics Overview
0:07
Vocabulary
0:27
Quotient
0:30
Rules for Dividing Integers
0:49
1:03
1:36
Rules for Dividing Integers, cont.
2:06
Arithmetic (Different Signs Integers)
2:14
Algebraic (Different Signs Integers)
2:41
Dividing Integer Examples
3:24
Dividing Integers: 14 ÷ 7
3:30
Dividing Integers: 45 ÷ (-9)
3:37
Dividing Integer Examples
3:51
Dividing Integers: (-105) ÷ (-15)
3:55
Dividing Integers: (-42) ÷ 6
5:07
Average Rate of Change
5:17
Using Integers to Represent the Situation
5:25
Example: Spend $360 in 6 Days 5:40 Example: Runs 1000 Feet in 4 Minutes 6:30 Average Rate of Change Word Problems 7:27 Example: Average Decrease in Value 7:32 Average Rate of Change Word Problems 9:19 Example: Average Increase in Stock 9:23 Average Rate of Change Word Problems 10:46 Example: Average Increase in Speed 10:51 Dividing Integers 12:00 Odd Number of Negatives 12:03 Even Number of Negatives 12:49 Order of Operations and Sign of Final Answer 13:50 Example: -120 ÷ (-5) ÷ -4 13:56 Extra Example 1: Order of Operations 14:48 Extra Example 2: Evaluate the Expression 15:29 Extra Example 3: Rate of Change 17:18 Extra Example 4: Rate of Evaporation 19:22 Positive Exponents 20m 5s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:26 Factor 0:32 Exponent 1:16 Vocabulary 1:57 Base 1:58 Power 2:18 Writing Expressions with Exponents 2:31 Example 1: Writing Expressions with Exponents 2:36 Example 2: Writing Expressions with Exponents 3:00 Writing Expressions with Exponents 3:20 Example 3: Writing Expressions with Exponents 3:25 Example 4: Writing Expressions with Exponents 3:53 Simplifying Power 4:06 Example 5: Simplifying Power 4:14 Example 6: Simplifying Power 5:03 Simplifying Power 6:06 Example 7: Simplifying Power 6:09 Example 8: Simplifying Power 6:50 Order of Operations 7:24 PEMDAS 7:26 Order of Operations 8:32 Multiplying/Dividing and Adding/Subtracting 8:34 Evaluating Expressions with Exponents 10:07 Example 9: Evaluating Expressions with Exponents 10:11 Example 10: Evaluating Expressions with Exponents 11:07 Extra Example 1: Evaluate 12:33 Extra Example 2: Evaluate 13:42 Extra Example 3: Height of the Rocket 15:00 Extra Example 4: Number of Cells 16:38 Section 3: Equations and Applications Solving Addition Equations 21m 47s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:18 Equation 0:21 Isolate 1:00 Inverse Operations 1:18 Subtraction Property of Equality 1:59 Arithmetic 2:12 Algebraic 2:53 Inverse Operations 3:32 Example: 38 + x = 42 3:40 Using Substitution to Check Answer 4:43 Inverse Operations 5:19 Example: y + 7.3 = 9.1 5:22 Using Substitution to Check Answer 5:53 Draw a Model 6:26 Weight Gain 6:42 Draw a Model 8:20 Mountain Climber 8:23 Examples by Writing Equations 10:25 Calculating Profit: Sweat Shirt 10:30 Examples by Writing Equations 11:37 Calculating Profit: Car Dealer 11:38 Extra Example 1: Inverse Operation 14:21 Extra Example 2: Inverse Operation 15:37 Extra Example 3: Real Estate 17:23 Extra Example 4: Birth Date 20:06 Solving Subtraction Equations 19m 34s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:07 Vocabulary 0:23 Addition Property of Equality: Arithmetic 0:31 Addition Property of Equality: Algebraic 1:14 Subtraction Property of Equality: Arithmetic 1:54 Subtraction Property of Equality: Algebraic 2:19 Solving an Equation by Adding 3:05 Example: b - 2 = 2 3:22 Example: 23 - j = 12 4:00 Solving an Equation by Adding 5:29 Example: a - 7.9 = 17.9 5:32 Example: -5.6 + x = 10.2 6:33 Solving an Equation by Writing an Equation 7:42 Example: Bank Withdrawal 7:48 Solving an Equation by Writing an Equation 9:21 Example: Temperature 9:23 Extra Example 1: Solving Subtraction Equations 11:50 Extra Example 2: Solving Subtraction Equations 12:46 Extra Example 3: Money 13:40 Extra Example 4: Selling Price 16:01 Solving Multiplication and Division Equations 26m 11s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:19 Division Property of Equality: Arithmetic 0:27 Division Property of Equality: Algebraic 1:05 Multiplication Property of Equality: Arithmetic 1:38 Multiplication Property of Equality: Algebraic 2:07 Vocabulary 2:49 Inverse Operations 2:53 Solve the Equation Using Division 3:09 Example: 8x = 56 3:12 Example: -6y = 42 3:59 Solve the Equation Using Division 4:47 Example: 0.9c = 1.89 4:53 Solve the Equation Using Division 6:11 Example: Saving Money 6:17 Example: Soccer Team 8:14 Solve the Equation Using Multiplication 9:56 Example: a/7 = 9 10:04 Example: t/1.7 = 6 10:52 Solve the Equation Using Multiplication 12:09 Example: y/-45 = 3.2 12:17 Example: -p = 14 13:13 Solve the Equation Using Multiplication 14:10 Example: Distant 14:16 Extra Example 1: Solve the Equation 15:58 Extra Example 2: Solve the Equation 17:25 Extra Example 3: Height of an Elephant 20:55 Extra Example 4: Money 23:07 Solving Two-Step Equations 19m 10s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Two-Step Equation Involvement 0:19 Solving Two-Step Equations 0:41 Example: 8y - 11 = 32 0:45 Example: 32 = t/5 + 8 2:55 Solving Two-Step Equations 4:49 Example: Recommended Daily Intake 4:59 Solving Two-Step Equations 7:01 Example: Cost of Each Ride 7:02 Extra Example 1: Solving Two-Step Equations 10:13 Extra Example 2: Solving Two-Step Equations 12:54 Extra Example 3: Length of Phone Call 13:56 Extra Example 4: Cost of Owning a Pet 16:40 Square Roots 12m 16s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:16 Perfect Square 0:20 Square Root 0:46 Square Roots 1:13 Every Positive Number has Two Square Roots 1:14 Square Roots of a Number are Opposites 1:40 Square Root Symbol 1:54 Positive Square Root of a Number 1:56 Compare: √25 and -√25 2:08 Find the Square Root 2:50 Example: Square Root of 81 2:52 Example: Square Root of 121 3:13 Estimating Square Roots 3:29 Example: Square Root of 23 3:35 Example: Square Root of 390 4:13 Example: Negative Square Root of 125 4:50 Estimating Square Roots 5:27 Estimating Length 5:31 Simplifying Square Roots 7:05 Example: Square Root of 36 7:08 Example: Simplifying Square Roots 7:47 Extra Example 1: Estimate the Length 8:21 Extra Example 2: Simplify the Expression 9:05 Extra Example 3: Estimate the Length 9:50 Extra Example 4: Simplify the Expression 10:34 Pythagorean Theorem 14m 49s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:36 Right Triangle 0:39 Legs 0:57 Hypotenuse 1:02 Pythagorean Theorem 1:11 Arithmetic Example 1:12 Algebra Example 2:41 Find the Length of the Hypotenuse 3:04 Example 1: Hypotenuse of a Triangle 3:07 Example 2: Hypotenuse of a Triangle 4:30 Find the Length of the Hypotenuse 6:18 Example 3: Hypotenuse of a Right Triangle 6:19 Extra Example 1: Square Roots 8:41 Extra Example 2: Perimeter 9:43 Extra Example 3: Length of Screen 11:58 Extra Example 4: Length of Wire 13:14 Using the Pythagorean Theorem 16m 15s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:30 The Pythagorean Theorem 0:32 Find the Length of a Leg 1:14 Example 1: Length of Ramp 1:19 Example: 2 Length of Platform 4:22 Identifying a Right Triangle 6:13 Example 3: Determine Right Triangle 6:14 Example 4: Determine Right Triangle 8:08 Extra Example 1: Find the Missing Leg Length 10:04 Extra Example 2: Length of Ladder 11:39 Extra Example 3: Determine Given Lengths 13:04 Extra Example 4: Length of Pole 14:20 Section 4: Rational Numbers Prime Factorization 16m 40s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:23 Factor 0:24 Composite Number 1:04 Vocabulary 1:17 Prime Number 1:18 Prime Factorization 1:57 Divisibility Rules 2:54 Divisibility Rules for 2, 3, 4 ,5 ,6, 9 and 10 2:55 Finding Factors 4:56 Possible Arrangements 4:59 Finding Factors 6:06 How Many Oranges? 6:07 Prime or Composite 6:43 Prime or Composite: 48 6:47 Prime or Composite: 53 7:09 Prime or Composite: 57 7:35 Prime Factorization 8:16 Prime Factorization of 42 8:23 Prime Factorization of 84 8:47 Find the Number 9:23 Find the Number with the Given Prime Factorization 9:24 Extra Example 1: Prime or Composite 11:04 Extra Example 2: Prime Factorization of 72 12:23 Extra Example 3: Marching Arrangements 12:56 Extra Example 4: Flowers Arrangements 14:50 Greatest Common Divisor 14m 16s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:41 Factor 0:43 Common Divisor 1:00 Greatest Common Divisor (GCD)/ Greatest Common Factor (GCF) 1:16 Find the GCD by Listing Divisors 1:34 GCD of 27 and 36 1:46 GCD of 18 and 49 2:52 Prime Factorization to Find GCD 3:30 GCD of 42 and 72 3:42 GCD of 21 and 63 4:46 GCD in Word Problems 5:30 Greatest Number of Police Officers 5:32 GCD in Word Problems 7:15 Cutting Two Pipes 7:16 Extra Example 1: GCD of 32, -24, 40 8:08 Extra Example 2: How Many Groups? 9:41 Extra Example 3: GCD of Two Prime Numbers 11:34 Extra Example 4: How Many Children? 12:26 Equivalent Fractions 11m 22s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:21 Equivalent Fractions 0:23 Simplest Form 1:15 Creating Equivalent Fractions 1:59 Method to Create Equivalent Fractions 2:00 Equivalent Fractions 2:18 Write Two Fractions Equivalent to 5/8 2:22 Write Two Fractions Equivalent to 2/14 3:12 GCD to Simplify 3:51 Find the GCD of 24 and 32 4:03 Write 24/32 in Simplest Form 4:43 Write -27/45 in Simplest Form 5:08 Writing a Fraction 6:04 Example: What Fraction of the Vehicles are Trucks? 6:11 Writing a Fraction 7:45 Example: What Fraction of the Seats are Empty? 7:55 Extra Example 1: Pizza 9:00 Extra Example 2: Driving Time 9:28 Extra Example 3: Simplest Form 10:29 Extra Example 4: Basketball Team 10:52 Equivalent Forms of Rational Numbers 20m 47s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:08 Vocabulary 0:30 Rational Number 0:31 Terminating Decimal 0:53 Repeating Decimal 1:04 Converting Decimals to Fractions 1:22 Write 0.47 as a Fraction 1:26 Write 0.48 as a Fraction 2:03 Write 0.245 as a Fraction 3:21 Converting Decimals to Fractions 4:20 Write 0.08 as a Fraction 4:30 Write 0.8 as a Fraction 4:53 Converting Fractions to Decimals 5:26 Write 1/2 as a Decimal 5:30 Write 6/33 as a Decimal 6:12 Write -9/5 as a Decimal 7:39 Converting Fractions to Decimals in Word Problems 8:19 Batting Average 8:23 Converting Fractions to Decimals in Word Problems 11:22 Cooking Festival 11:26 Extra Example 1: Write 0.038 as a Fraction 14:45 Extra Example 2: Write -13/7 as a Decimal 15:35 Extra Example 3: Batting Average 16:38 Extra Example 4: Rational Number 19:55 Comparing and Ordering Rational Numbers 20m 21s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:29 Least Common Multiple (LCM) 0:30 Least Common Denominator (LCD) 1:50 Ordering Rational Numbers 2:45 Numbers as Decimals 2:46 Numbers as Fractions 5:36 Compare Each Pair of Numbers 8:10 Compare 3/4 and 4/5 8:11 Compare 3/11 and 1/6 8:44 Comparing rational Numbers in Word Problems 9:19 Cookies or French Fries? 9:22 Extra Example 1: Least to Greatest (Decimals) 11:32 Extra Example 2: Least to Greatest (Fractions) 13:35 Extra Example 3: Music Notes 15:54 Extra Example 4: Chocolate or Fruit 17:16 Section 5: Rational Number Operations Adding Rational Numbers 15m 4s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:19 Least Common Multiple (LCM) 0:20 Least Common Denominator (LCD) 0:28 Adding Fractions with Unlike Denominators 1:22 Example: 3/4 + 2/5 1:28 Example: -3/5 + 1/7 2:29 Adding Different Forms of Rational Numbers 3:23 Example: Change to Fractions 3:31 Example: Change to Decimals 5:14 Extra Example 1: Adding Different Forms of Numbers 7:02 Extra Example 2: Exercising 10:06 Extra Example 3: Adding Different Forms of Numbers 11:20 Extra Example 4: Cooking Recipe 13:47 Subtracting Rational Numbers 14m 40s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:19 Least Common Denominator (LCD) 0:20 Subtracting with Unlike Denominators 0:41 Example: 5/9 - 3/5 0:44 Example: 3/4 - 7/8 1:23 Subtracting Rational Numbers 1:59 Example: 23/4 - 3.5 2:05 Example: 11.7 - 3/4 3:39 Subtracting Rational Numbers in Word Problems 4:37 Puppy's Weight 4:41 Extra Example 1: Subtracting with Unlike Denominators 6:48 Extra Example 2: Subtracting Rational Numbers 7:27 Extra Example 3: Rainfall 10:32 Extra Example 4: Decorating Your House 12:06 Multiplying Rational Numbers 11m 2s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:17 Rational Number 0:18 Exponent 0:30 Power 0:35 Multiplying Decimals 0:47 Example 1: Multiplying Decimals 0:50 Example 2: Multiplying Decimals 1:18 Multiplying Rational Numbers in Word Problems 1:51 Example: Length of Pipes 1:56 Raising a Fraction to a Power 2:58 Examples: Raising Fractions to Power 2:59 Extra Example 1: Multiplying Fractions 4:45 Extra Example 2: Compare Fractions 5:34 Extra Example 3: Flour 7:28 Extra Example 4: Income 8:50 Dividing Rational Numbers 12m 8s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:22 Reciprocal 0:26 Finding the Reciprocal 0:56 Example: Reciprocal of 2/3 1:00 Example: Reciprocal of 8 1:04 Example: Reciprocal of -1/2 1:10 Dividing Rational Numbers 1:28 Example 1: Dividing Rational Numbers 1:35 Example 2: Dividing Rational Numbers 2:09 Example 3: Dividing Rational Numbers 2:35 Dividing Rational Numbers in Word Problems 3:56 Example: Chocolate Peanuts 4:00 Extra Example 1: Dividing Decimals 5:17 Extra Example 2: Dividing Fractions 7:09 Extra Example 3: Search Committee 8:34 Extra Example 4: Stake 10:18 Solving Equations by Adding or Subtracting 13m 43s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 What You'll Learn and Why 0:23 Isolate 0:24 Solving Equations with Fractions 0:41 Example: n + 1/2 = 11/12 0:44 Example: 3/5 - a = 13/20 1:34 Writing Equations with Fractions 3:08 Example: Thickness 3:11 Extra Example 1: Solving Equations 6:01 Extra Example 2: Solving Equations 6:58 Extra Example 3: School Lunches 8:23 Extra Example 4: Fashion Designer 10:44 Solving Equations by Multiplying 11m 10s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:20 Multiplicative Inverse 0:21 Solve Each Equation 0:51 Example 1: Solve the Equation 0:57 Example 2: Solve the Equation 2:39 Writing Multiplication Equations 3:30 Example: Water Level 3:34 Extra Example 1: Solve the Equation 5:15 Extra Example 2: Solve the Equation 6:28 Extra Example 3:Money 7:26 Extra Example 4: Solve the Equation 9:45 Zero and Negative Exponents 6m 41s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:22 Zero Exponents: Arithmetic Definition 0:27 Zero Exponents: Algebra Definition 0:39 Negative Exponents: Arithmetic Definition 0:46 Negative Exponents: Algebra Definition 1:03 Simplifying Exponents 1:18 Examples: Simplifying Exponents 1:21 Fractions and Negative Exponents 2:41 Examples: Fractions and Negative Exponents 2:45 Extra Example 1: Negative Exponent 3:58 Extra Example 2: Zero Exponent 4:30 Extra Example 3: Fraction and Negative Exponent 4:40 Extra Example 4: Subtracting Numbers with Exponents 5:00 Section 6: Rates and Proportions Ratios 7m 5s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:22 Ratio 0:23 Equivalent Ratios 0:40 Writing a Ratio 1:18 Write the Ratio in Three Ways 1:21 Writing an Equivalent Ratio 2:07 Different Ratios Equivalent to 10:12 2:08 Writing a Ratio in Simplest Form 2:47 Write the Ratio in Simplest Form 2:50 Extra Example 1: Write the Ratio 3:32 Extra Example 2: Ratio in Simplest Form 4:38 Extra Example 3: Write the Ratio 5:08 Extra Example 4: Ratio in Simplest Form 5:48 Rates 12m 45s Intro 0:00 What You'll Learn and Why 0:04 Topics Overview 0:05 Vocabulary 0:18 Rate 0:22 Unit Rate 0:40 Finding a Unit Rate 1:00 Example: Delivery Rate 1:03 Using a Unit Rate 1:46 Example: Miles and Gallon of Gas 1:49 Comparing Unit Rates 2:52 Example: Which is the Better Buy 2:58 Extra Example 1: Calories 6:30 Extra Example 2: Typing Speed 7:22 Extra Example 3: Which is the Better Buy 8:23 Extra Example 4: Wages 10:48 Dimensional Analysis 16m 19s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:15 Conversion Factor 0:16 Dimensional Analysis 0:23 Conversion Chart: Length 0:32 Conversion Chart: in, ft, yd, and m 0:33 Conversion Chart: Weight 0:49 Conversion Chart: oz, lb, and t 0:50 Conversion Chart: Capacity 0:59 Conversion Chart: fl oz, cup, pt, qt, and gal 1:00 Converting Units 1:17 Example: Convert 1.3 Miles Into Feet 1:18 Converting Units 3:14 Example: Convert Pounds to Ounces 3:15 Example: Convert Cups to Fluid Ounces 3:52 Converting Units in a Rate 4:30 Unit Rate: 2,200 m in 17.2 min 4:31 Using Dimensional Analysis 8:06 Example: Planning Project 8:07 Extra Example 1: Converting Units 9:15 Extra Example 2: Unit Rate 10:31 Extra Example 3: Planning Project 12:15 Extra Example 4: Converting Units 13:45 Application of Rates 17m 42s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:18 Rate 0:22 Unit Rate 0:27 Finding Total Distance 0:32 Example: Total Distance 0:33 Finding Average Speed 2:49 Example: Car's Average Speed 2:53 Using a Unit Rate 6:31 Example: Weight and Spring 6:32 Extra Example 1: Total Distance 8:08 Extra Example 2: Bird's Average Speed 10:33 Extra Example 3: Cost of Shirts 13:37 Extra Example 4: Cost of Bottles 15:22 Proportions 14m 36s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:16 Proportion 0:17 Cross Products 0:45 Identifying a Proportion 11:28 Example: Do the Ratios Form a Proportion? 11:29 Solving Proportions Using Two Methods 2:47 Example: x/4 = 12/21 3:03 Example: 20/y = 15/9 4:43 Solving Proportions in Word Problems 5:56 Example: Find the Unit Rate of Exchange 6:00 Extra Example 1: Does the Ratio Form a Proportion? 9:55 Extra Example 2: Solving Proportions 10:53 Extra Example 3: Find the Length of the Photo 11:33 Extra Example 4: Distance 12:59 Section 7: Applications of Percent Fractions, Decimals, and Percents 10m 13s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:24 Percent 0:25 Compare a Fraction to a Decimal to a Percent 0:35 Example: 31 out of 100 0:39 Write a Percent as a Fraction 1:11 Example: Write 47% as a Fraction 1:12 Example: Write 25% as a Fraction 1:59 Write a Fraction as a Percent 2:38 Example: Write 2/10 as a Percent 2:39 Example: Write 57/100 as a Percent 3:22 Example: Write 3/25 as a Percent 3:57 Write a Decimal as a Percent 4:48 Example: Write 0.85 as a Percent 4:49 Example: Write 0.3 as a Percent 5:05 Example: Write 0.04 as a Percent 5:17 Extra Example 1: Write Percent as Decimal and Fraction 5:34 Extra Example 2: Write Fraction as Decimal and Percent 6:47 Extra Example 3: Write Percent as Fraction and Decimal 7:41 Extra Example 4: Fraction, Percent, and Decimal of Students 8:36 Finding a Percent of a Number 8m 39s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:20 Percent 0:21 Finding a Percent 0:26 Example: Find 15% of 100 0:27 Example: Find 10% of 135 1:08 Finding More Percents 2:23 Example: Find 8% of 65 2:25 Example: Find 120% of 50 2:45 Estimating a Percent 3:25 Example: Estimate 10% of 31.05 3:38 Example: Estimate 15% of 31.05 3:54 Example: Estimate 20% of 31.05 4:55 Extra Example 1: Find 7% of 120 5:35 Extra Example 2: Find 125% of 75 6:01 Extra Example 3: Estimate 15% Tip 7:02 Extra Example 4: Estimate 20% Tip 8:01 Percents and Proportions 15m 38s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:23 Proportion 0:33 Cross Products 0:38 Finding Part of a Whole 1:07 Method 1: Find 50% of 36 1:11 Method 2: Find 50% of 36 2:23 Finding Part of a Whole, cont. 3:06 Example: Find 65% of 143 3:07 Finding the Whole Amount 3:44 Example: How Many Students are in 8th Grade? 3:45 Finding the Whole Amount, cont. 5:18 Example: How Many Students are in the School? 5:19 Finding a Percent 6:38 Method 1: What Percent of 175 is 105 7:21 Method 2: What Percent of 175 is 105 8:49 Finding a Percent, cont. 9:57 What Percent of 115 is 46? 9:58 Extra Example 1: Find 8% of 48 11:09 Extra Example 2: 9 is 25% of What Number? 11:34 Extra Example 3: How Many Students are in the Class? 12:39 Extra Example 4: 66 is What Percent of 55? 14:25 Percent of Change 11m 27s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:17 Percent of Change 0:18 Amount of Change/ Original Amount 0:26 Finding a Percent of Increase 1:04 Example: Find the Percent of Increase 1:06 Converting Units 2:56 Example: Converting Units and Percent Increase 3:00 Finding a Percent of Decrease 5:08 Example: Find the Percent of Decrease 5:09 Extra Example 1: Find the Percent of Increase 6:32 Extra Example 2: Find the Percent of Decrease 7:30 Extra Example 3: Find the Percent of Increase 8:28 Extra Example 4: Find the Percent of Decrease 10:23 Applications of a Percent 12m 55s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:22 Markup 0:23 Selling Price 0:28 Formula of Markup 0:32 Formula for Discount 1:06 Finding a Percent of Markup 1:16 Example: Find the Percent of Markup 1:19 Finding a Percent of Discount 3:19 Example: Find the Percent of Discount 3:21 Finding a Sale Price 5:03 Example: Find the Sale Price of the Stereo System 5:10 Extra Example 1: Find the Percent of Markup 6:39 Extra Example 2: Find the Percent of Discount 8:57 Extra Example 3: Find the Percent of Discount 9:52 Extra Example 4: Find the Percent of Discount 10:44 Section 8: Linear Functions and Graphing Graphing in the Coordinate Plane 15m 13s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:17 Coordinate Plane 0:23 y-axis 0:29 x-axis 0:33 Quadrants 0:37 More Vocabulary 0:49 Origin 0:50 Ordered Pair 0:53 x-coordinate 1:00 y-coordinate 1:08 Labeling Vocabulary 1:24 Example: Label the Vocabulary 1:25 Graphing Points on a Coordinate Plane 3:08 Example: Graph and Label the Locations 3:12 Quadrants 6:18 Example: Name the Quadrants of Each Ordered Pair 6:23 Extra Example 1: Draw and Label 10:18 Extra Example 2: Graph the Ordered Pair 11:20 Extra Example 3: Graph the Ordered Pair 12:42 Extra Example 4: Name the Quadrants of Each Ordered Pair 13:32 Length in the Coordinate Plane 18m 36s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:18 x-coordinate 0:21 y-coordinate 0:28 Pythagorean Theorem 0:34 Finding Lengths of Line Segments 1:02 Example: Find the Length of the Horizontal Line Segment 1:05 Finding Lengths of Line Segments 3:50 Example: Find the Length of the Vertical Line Segment 3:54 Finding Distance in the Coordinate Plane 5:59 Example: Find the Length of the Hypotenuse 6:02 Extra Example 1: Find the Distance Between Two Points 7:36 Extra Example 2: Find the Length of the Line Segment 10:13 Extra Example 3: Find the Length of the Line Segment 14:28 Extra Example 4: How Far is Your School from the Arcade? 16:02 Functions 14m 29s Intro 0:00 What You'll Learn and Why 0:04 Topics Overview 0:05 Vocabulary 0:24 Function 0:25 Function Rule 0:51 Evaluating a Function Rule 0:59 Example: Table of Input and Output 1:00 Using Function Notation 2:56 Example: Write the Equation and Evaluate the Cost 2:59 Writing Functions 4:40 Example: Writing Function 4:41 Extra Example 1: Complete the Table 6:02 Extra Example 2: Complete the Table and Find the Function 7:38 Extra Example 3: Function Notation 9:39 Extra Example 4: Write a Function and Find the Total Cost 11:49 Graphing Linear Functions 16m 2s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:21 Solution 0:22 Linear Equation 0:29 Linear Function 0:44 Making a Graph from a Table 1:05 Example: Total Savings in Dollars 1:08 Graphing a Linear Function 3:03 Example: Graph the Linear Function 3:07 Extra Example 1: How Much Cereal is Left? 5:42 Extra Example 2: Graph the Value 7:45 Extra Example 3: Graph the Linear Function 10:17 Extra Example 4: Graph the Linear Function 12:28 Slope 17m 53s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:15 Slope Definition 1 0:18 Slope Definition 2 0:40 Slope 1:20 Positive Slope 1:32 Negative Slope 1:39 Slope of 0 2:10 Undefined Slope 2:25 Finding the Slope of a Line 3:57 Example: Using Rise/Run to Find Slope 3:58 Finding the Slope of a Line 6:01 Example: Using Coordinates to Find Slope 6:02 Finding Slope of a Line With Given Coordinates 9:00 Example: Slope of (4,1) and (3, -2) 9:01 Extra Example 1: Find the Slope of the Line 10:17 Extra Example 2: Find the Slope of the Line 12:19 Extra Example 3: Find the Slope of the Line 14:54 Extra Example 4: Find the Slope of the Line 16:35 Slope and Direct Variation 13m 50s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:33 Direct Variation 0:34 Identifying a Direct Variation 0:47 Steps in Identifying a Direct Variation 0:56 Slope and Direct Variation 3:01 Example: Slope and Direct Variation 3:05 Extra Example 1: Direct Variation 6:16 Extra Example 2: Direct Variation 7:14 Extra Example 3: Graphing Direct Variation 8:10 Extra Example 4: Slope and Direct Variation 11:23 Section 9: Inequalities Writing Inequalities 17m 32s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:15 Inequality 0:18 System of Inequalities 1:31 Solution of an Inequality 1:50 Writing an Inequality 2:10 Example: Price p is More than$6
2:20
Writing an Inequality
3:53
Example: Wage w is at Least $8.25 3:54 Writing a System of Inequalities 5:24 Example: System of Inequalities for Wind Speed 5:32 Writing a System of Inequalities 9:03 Example: Price of a Room in Las Vegas 9:04 Identifying Solutions of an Inequality 10:33 Example: Driver's Permit 10:37 Extra Example 1: Writing Inequalities 12:03 Extra Example 2: Writing a System of Inequalities 13:24 Extra Example 3: Writing Inequalities 14:51 Extra Example 4: Using Inequality to Solve Word Problem 15:31 Solving Inequalities by Adding or Subtracting 9m 16s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:20 Addition Property of Equality 0:31 Subtraction Property of Equality 0:43 Example: x > 7 0:57 Solving an Inequality by Adding 1:33 Example: Solve x - 8 = 10 1:37 Example: Solve x - 8 < 10 2:05 Solving an Inequality by Adding 2:21 Example: 2 ≤ t - 5 2:22 Example: a - 8 > 15 2:59 Solving an Inequality by Subtracting 3:14 Example: How Many Students can Board the Bus? 3:22 Solving an Inequality by Subtracting 4:13 Example: How Many More Tickets can be Sold? 4:14 Extra Example 1: Solve the Inequality 5:16 Extra Example 2: Solve 8 ≥ 3 + m 5:52 Extra Example 3: MP3 Player 6:29 Extra Example 4: Write and Solve an Inequality 7:34 Solving Inequalities by Dividing 12m 15s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:22 Division Property of Inequality 0:23 Example: 3x > 6 0:37 Dividing by a Positive Number 1:08 Example: Hotel Elevator 1:11 Dividing by a Negative Number 2:29 Example: Solve -6x ≥ -18 2:32 Example: Suppose x = 2 3:13 Dividing by a Negative Number 4:58 Example: Solve -3t ≥ 51 5:05 Example: Solve -8m < -56 5:24 Extra Example 1: Photo Album 5:49 Extra Example 2: Banquet 8:05 Extra Example 3: Solve -0.5x > 18 9:24 Extra Example 4: How Many Crates can the Crane Lift? 10:30 Solving Inequalities by Multiplying 14m 33s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:17 Multiplication Property of Inequality 0:18 Multiplying by a Positive Number 1:25 Example: Write and Solve an Inequality 1:28 Multiplying by a Positive Number 3:38 Example: Write and Solve an Inequality 3:39 Multiplying by a Negative Number 5:42 Example: Solve x/-4 > 28 5:45 Example: Solve (-1/2)y < -8 6:10 Example: t/-7 < 5 6:42 Extra Example 1: Bowling League 7:12 Extra Example 2: Street Performers 8:27 Extra Example 3: Write and Solve the Inequality 9:52 Extra Example 4: Solve and Graph the System of Inequalities 11:26 Solving Two-Step Inequalities 14m 15s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:15 Inequality 0:16 Properties of Inequality 0:27 Solving Two-Step Inequalities 0:37 Example: Solve -2x - 8 > -14 0:41 Example: Solve (x/4) - 7 > 25 1:40 Example: Solve -5y + 9 ≤ 54 2:12 Writing Two-Step Inequalities 3:16 Example: How Many Pairs of Socks? 3:21 Writing Two-Step Inequalities 5:49 Example: How Many Folders? 5:53 Extra Example 1: Solve 15 < -3 ( x + 1 ) 7:32 Extra Example 2: Solve the Inequalities 8:43 Extra Example 3: Muffin 10:37 Extra Example 4: Birthday Party 11:51 Section 10: Exponents and Equations Properties of Exponents 12m 7s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:26 Exponent 0:29 Power 0:44 Multiplying Powers with the Same Base 1:04 Example: Multiplying Powers with the Same Base 1:07 Multiplying Expressions with Exponents 2:25 Examples 2:26 Dividing Powers with the Same Base 3:24 Example: Dividing Powers with the Same Base 3:25 Dividing Expression with Exponents 3:59 Example: How Long Sunlight Takes to Reach the Comet 4:02 Dividing Expression with Exponents 6:44 Example: How Long Sunlight Takes to Reach Earth 6:45 Extra Example 1: Multiplying Expressions with Exponents 8:22 Extra Example 2: Dividing Expression with Exponents 8:46 Extra Example 3: How Long Sunlight Takes to Reach Saturn 9:12 Extra Example 4: Sun's Diameter and Earth's Diameter 10:34 Power Rules 11m 58s Intro 0:00 What You'll Learn and Why 0:04 Topics Overview 0:05 Vocabulary 0:15 Exponent 0:18 Power 0:34 Raising a Power to a Power 0:44 Example: Raising a Power to a Power 0:47 Raising a Power to a Power 2:38 More Examples 2:42 Raising a Product to a Power 3:00 Example: Raising a Product to a Power 3:01 Raising a Product to a Power 4:00 Example: Surface Area of a Plant Cell 4:12 Example: Surface Area of the Moon 6:15 Extra Example 1: Raising Power to a Power 8:08 Extra Example 2: Complete the Inequality Statement 8:22 Extra Example 3: Find the Area of a Square 8:51 Extra Example 4: Find the Area of a Circle 10:28 Exploring Roots 9m 39s Intro 0:00 What You'll Learn and Why 0:05 Topics Overview 0:06 Vocabulary 0:17 Square Root 0:21 Roots 1:13 The Root Symbol 2:10 Root Symbols 2:11 Finding Roots of a Number 2:41 Examples 2:42 Simplifying Expressions with Roots 4:41 Example: Simplify the Expression 4:42 Simplifying Expressions with Roots 5:42 Example: Simplify the Expression 5:43 Extra Example 1: Finding Roots of a Number 6:36 Extra Example 2: Simplifying Expressions with Roots 7:11 Extra Example 3: Simplifying Expressions with Roots 7:36 Extra Example 4: Simplifying Expressions with Roots 8:34 Simplifying Algebraic Expressions 12m 43s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:23 Term 0:28 Like Terms 0:35 Combining Like Terms 1:18 Example: 2y + y - 15y 1:20 Example: -x - 5x 2:16 Writing and Simplifying Expressions 2:57 Example: Total Cost of Drinks 2:58 Writing and Simplifying Expressions 4:48 Example: Total Cost of Apples 4:49 Distributing and Simplifying 5:42 Simplify: 4x - 2( x + 6 ) 5:46 Simplify: 3( 2y + 2 ) - 4y 6:57 Extra Example 1: Simplify the Expression 7:52 Extra Example 2: Distributing and Simplifying 8:18 Extra Example 3: Writing and Simplifying Expressions 9:35 Extra Example 4: Distributing and Simplifying 10:50 Solving Multi-Step Equations 18m 35s Intro 0:00 What You'll Learn and Why 0:06 Topics Overview 0:07 Vocabulary 0:17 Like Terms 0:21 Distributive Property 0:49 Simplifying Before Solving an Equation 1:37 Example: 8x + 45 - 12x = 9 1:40 Example: -15 = 6b + 12 - 3b + 6 3:25 Using the Distributive Property 4:50 Example: Haiti Relief Efforts 4:51 Using the Distributive Property 7:50 Example: Amusement Park 7:51 Extra Example 1: Simplify and Solve 11:34 Extra Example 2: Simplify and Solve 12:21 Extra Example 3: Simplify and Solve 13:18 Extra Example 4: Mailing Letters 14:53 Solving Equations with Variables on Both Sides 18m 50s Intro 0:00 What You'll Learn and Why 0:07 Topics Overview 0:08 Vocabulary 0:26 Term 0:30 Like Terms 0:44 Variables on Both Sides 1:10 Example: 3x + 24 = 9x 1:11 Example: -7 - 3x = 1 + 5x 2:16 Using the Distributive Property 4:01 Example: Height of Two Plants 4:02 Using the Distributive Property 9:01 Example: Running Laps 9:02 Extra Example 1: Solving Equations with Variables on Both Sides 11:59 Extra Example 2: Solving Equations with Variables on Both Sides 12:46 Extra Example 3: Solving Equations with Variables on Both Sides 14:18 Extra Example 4: Cost of Renting Video 15:24 Section 11: Test-Taking Strategies Test Taking Strategy Part 1 12m 55s Intro 0:00 Finding Needed Information 1:02 Ask Yourself 1:07 Example: Finding Needed Information 1:25 Extra Example 1: Finding Needed Information 2:36 Extra Example 2: Finding Needed Information 4:10 Using Mental Math 6:10 Use Mental Math to Eliminate Unreasonable Answers 6:16 Example: Using Mental Math 6:47 Extra Example 1: Simplify Using Mental Math 8:54 Extra Example 2: Mental Math and Total Cost 9:36 Extra Example 3: Account Balance 11:15 Test Taking Strategy Part 2 11m 24s Intro 0:00 Working Backward 0:06 Substitute Multiple Choice Answers 0:08 Example: Working Backward 0:38 Extra Example 1: Equivalent Expression 2:54 Extra Example 2: Miles Per Gallon 4:13 Extra Example 3: Miles Per Hour 5:14 Choosing the Process 6:12 Strategies for Choosing the Process 6:19 Example: Dimensions of the Fenced Area 6:48 Extra Example 1: Choosing the Process 8:28 Extra Example 2: Choosing the Process 10:01 Test Taking Strategy Part 3 11m 36s Intro 0:00 Eliminating the Answer 0:06 Eliminate Wrong Answers 0:07 Example: Height of a Plant 0:49 Extra Example 1: Distance 2:36 Extra Example 2: Decimal 4:11 Using a Variable 4:50 Variables Represent the Unknown 4:51 Example: Company Logo 5:20 Extra Example 1: Road Trip 6:31 Extra Example 2: Proportion 9:03 Test Taking Strategy Part 4 20m 13s Intro 0:00 Eliminating the Answer 0:06 Eliminate Answers and Educated Guess 0:07 Example: Election 0:28 Extra Example 1: Football Kicker 2:42 Extra Example 2: Percent 4:09 Answering the Question Asked 6:19 Answer the Question Correctly 6:20 Example: Inequality 6:43 Extra Example 1: Cost of Cheese 8:12 Extra Example 2: Inequality 9:40 Drawing a Diagram 11:35 Diagrams 11:36 Example: Drawing a Diagram to Show Distance 12:03 Extra Example 1: Drawing a Diagram to Show Distance 15:22 Extra Example 2: Height 17:48 Loading... This is a quick preview of the lesson. For full access, please Log In or Sign up. For more information, please see full course syllabus of Pre Algebra Bookmark & Share Embed ## Share this knowledge with your friends! ## Copy & Paste this embed code into your website’s HTML Please ensure that your website editor is in text mode when you paste the code. (In Wordpress, the mode button is on the top right corner.) × • - Allow users to view the embedded video in full-size. Since this lesson is not free, only the preview will appear on your website. • ## Discussion • ## Answer Engine • ## Study Guides • ## Practice Questions • ## Download Lecture Slides • ## Table of Contents • ## Related Books Lecture Comments (5)  2 answersLast reply by: Kyle SuFri Nov 22, 2019 11:20 PMPost by Danny Fanny on November 20, 2014Good Job 1 answerLast reply by: Professor FungSat Dec 1, 2012 4:01 AMPost by bo young lee on November 29, 2012i dont know how t0 slove question using a formula that have the verticla change and horizontal change . ### Slope and Direct Variation • Direct variation is a linear function in the form y = kx, where k ≠ 0. • The variable y and x have a constant ratio, meaning that they vary directly. • The slope of the graph of two quantities is a ratio that is equal to the direct variation. • Remember that slope is the ratio of rise over run; change in y divided change in x. ### Slope and Direct Variation The relationship between the number of pounds of apples squeezed, x, and the ounces of apple juice made, y, is a linear function. The table shows some solutions to the function. Is the function a direct variation?  Input (x) Output (y) 3 9 5 15 9 27 10 30 • The ratio of the two quantities is [3/1] • The slope is always [3/1] • Since the ratio and the slope are equal, the function is a direct variation Yes A store sells apples for$ 1.75 per pound. Graph the relationship between the pounds of apples purchased, x, and the total cost, y. Find the slope of the line and explain what it represents.
• y = 1.75x
• Make a table to find the solutions:
•  Input (x) Output (y) 0 0 1 1.75
• Use two points to graph the line on a coordinate plane:
• Find the slope:
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (1,1.75)
• m = [(1.75 − 0)/(1 − 0)] =
Slope = 1.75
The slope represents the increase in cost for every increase of 1 pound of apples purchased. That is, for every pound of apples bought, the cost increases by \$ 1.75.
Is the linear function in this table a direct variation?
 Input (x) Output (y) 0 0 1 3.5 2 7 3 10.5
• The ratio of the two quantities is [3.5/1]
• The slope is always [3.5/1]
Yes
Is the linear function in this table a direct variation?
 Input (x) Output (y) 2 6 3 9 4 11 5 16
• [6/2] = 3
• [9/3] = 3
• [11/4] ≠ 3
• [16/5] ≠ 3
• The ratios aren't the same
No
Graph the direct variation y = − 2x and find the slope of the line.
• Make a table of x- and y - coordinates before graphing the equation.
•  Input (x) Output (y) 0 0 1 -2
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (1, − 2)
• m = [( − 2 − 0)/(1 − 0)] =
• [( − 2)/1] =

Slope = − 2
Suppose you eat 3 times each day. Graph the relationship between the number of days passed, x, and the cumulative number of meals you've eaten, y. Find the slope of the line and explain what it represents.
• y = 3x
•  Input (x) Output (y) 0 0 1 3 2 6
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (1,3)
• m = [(3 − 0)/(1 − 0)] =
• [3/1] =

Slope = 3
The slope represents the increase of cumulative meals eaten for every increase of a day passing. That is, for every day that goes by, 3 more meals are eaten.
Is the function in this table a direct variation?
 Input (x) Output (y) 1 5 2 6 3 7 4 8
• [5/1] = 5
• [6/2] = 3
• [7/3]
• [8/4] = 2
• The ratio of quantities are not the same.
No
Graph y = − 0.5x and find the slope of the line.
• Make a table of x- and y- coordinates before graphing the equation.
•  Input (x) Output (y) 0 0 2 1
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (2,1)
• m = [(1 − 0)/(2 − 0)] =

Slope = [1/2]
Graph the equation y = − 3x and find the slope of the line.
• Make a table of x- and y- coordinates before graphing the equation.
•  Input (x) Output (y) 0 0 1 -3
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (1, − 3)
• m = [( − 3 − 0)/(1 − 0)] =
• [( − 3)/1] =

Slope = − 3
Graph y = [1/3]x and find the slope of the line.
• Make a table of x- and y- coordinates before graphing the equation.
•  Input (x) Output (y) 0 0 3 1
• m = [(y1 − y2)/(x1 − x2)], (0,0) and (3,1)
• m = [(1 − 0)/(3 − 0)] =

Slope =[1/3]

*These practice questions are only helpful when you work on them offline on a piece of paper and then use the solution steps function to check your answer.

### Slope and Direct Variation

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

• Intro 0:00
• What You'll Learn and Why 0:05
• Topics Overview
• Vocabulary 0:33
• Direct Variation
• Identifying a Direct Variation 0:47
• Steps in Identifying a Direct Variation
• Slope and Direct Variation 3:01
• Example: Slope and Direct Variation
• Extra Example 1: Direct Variation 6:16
• Extra Example 2: Direct Variation 7:14
• Extra Example 3: Graphing Direct Variation 8:10
• Extra Example 4: Slope and Direct Variation 11:23

OR

### Start Learning Now

Our free lessons will get you started (Adobe Flash® required).

### Membership Overview

• *Ask questions and get answers from the community and our teachers!
• Practice questions with step-by-step solutions.