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Lecture Comments (6)

0 answers

Post by TAHA sakor on December 7, 2014

I didn't understand why the table starts with -2?

1 answer

Last reply by: Professor Fung
Wed Jun 5, 2013 3:42 AM

Post by bo young lee on December 5, 2012

i dont understand this question,
graph each equation by plotting ordered pairs.
y=3x-4

2 answers

Last reply by: Professor Fung
Wed Jun 5, 2013 3:19 AM

Post by Clinesha Phillips on December 4, 2012

Im having a hard time understanding linear functions in my pre-algebra class. I have an example one out of my book please show me how to do this problem. y= 1/2x - 4 thank you

Graphing Linear Functions

  • You can represent the relationship between two quantities, such as an input and output, by using a table, a rule or equation, or a graph.
  • In order to graph a linear equation create a table. Choose input values of your choice. In most situations, choose small values including zero. If the function includes a fraction you may want to choose multiples of the denominator so that you can simplify the fractions to whole numbers, which are easier to graph. The input value is the x-coordinate and the output value is the y-coordinate.
  • Any ordered pair that makes an equation true is a solution.

Graphing Linear Functions

Suppose you make $ 200 each week from your job. Make a table and a graph depicting the relationship between the number of weeks, x, and the total earnings in dollars, y.
Input (x) Output (y)
00
1200
2 400

Graph the linear function y = [1/4](x − 3) by first making a table.
  • y(0) = [1/4](0 − 3)
  • y(0) = [1/4]( − 3)
  • y(0) = − [3/4]
  • y(1) = [1/4](1 − 3)
  • y(1) = [1/4]( − 2)
  • y(1) = − [1/2]
  • y(2) = [1/4](2 − 3)
  • y(2) = [1/4]( − 1)
  • y(2) = − [1/4]
Input (x) Output (y)
0-0.75
1-0.5
2-0.25

Graph the linear function y = 2x − 4 by first making a table.
  • y(0) = 2(0) − 4
  • y(0) = 0 − 4
  • y(0) = − 4
  • y(1) = 2(1) − 4
  • y(1) = 2 − 4
  • y(1) = − 2
  • y(2) = 2(2) − 4
  • y(2) = 4 − 4
  • y(2) = 0
Input (x) Output (y)
0-4
1-2
20

Graph the linear function y = [1/4]x − 10 by first making a table.
  • y(4) = [1/4](4) − 10
  • y(4) = 1 − 10
  • y(4) = − 9
  • y(8) = [1/4](8) − 10
  • y(8) = 2 − 10
  • y(8) = − 8
  • y(12) = [1/4](12) − 10
  • y(12) = 3 − 10
  • y(12) = − 7
Input (x) Output (y)
4-9
8-8
12-7

Graph the values in the table. Then, connect the points with a line.
Input (x) Output (y)
04
20
3-2
5-6
  • The table gives the points (0,4), (2,0), (3, − 2), and (5, − 6)
Graph the linear function y = − 3x + 2
  • y(0) = 0 + 2 = 2 ⇒ (0,2)
  • y(1) = − 3 + 2 = − 1 ⇒ (1, − 1)
Graph the linear function y = [3/4]x + 2
  • y(0) = 0 + 2 = 2 ⇒ (0,2)
  • y(4) = [3/4](4) + 2 = 5 ⇒ (4,5)
Eric spends $ 47 a week on gas. Make a graph showing the relationship between weeks and the cumulative cost of gas.
Graph the equation y = 5x − 11
  • y(0) = 0 − 11 = − 11
  • y(1) = 5 − 11 = − 6
  • y(2) = 10 − 11 = − 1
Graph the equation y = [1/2]x + 3
  • y(0) = 0 + 3 = 3
  • y(1) = [1/2] + 3 = 3[1/2]

*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.

Answer

Graphing Linear Functions

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 0:21
    • Solution
    • Linear Equation
    • Linear Function
  • Making a Graph from a Table 1:05
    • Example: Total Savings in Dollars
  • Graphing a Linear Function 3:03
    • Example: Graph the Linear Function
  • 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