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### Slope and Rate of Change

- The
*slope*of a straight line is the ratio of the change in the y coordinates to the change in the x coordinates of two particular points that lie on the line. This is also known as a rate of change. - Slope is a measurement of how steep the line is. The larger the absolute value of the slope, the steeper the line.
- Any two points on a line can be used to compute the slope. The same value will be obtained, no matter which two points are chosen.
- The slope can be positive, negative, 0, or undefined.
- A horizontal line has slope 0. A vertical line has undefined slope.
- If a line increases as it moves from left to right, its slope is positive. If it decreases, its slope is negative.

### Slope and Rate of Change

Find the slope of the line passing through the points ( − 2, − 6) and (10, − 3)

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - slope = [( − 3 − ( − 6))/(10 − ( − 2))]
- slope = [3/12]

slope = [1/4]

Find the slope of the line passing through the points (15, − 9) and ( − 11, − 7)

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - slope = [( − 7 − ( − 9))/( − 11 − 15)]

slope = [2/( − 26)]

Find the slope of the line passing through the points ( − 8,4) and ( − 12, − 3)

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - slope = [( − 3 − 4)/( − 12 − ( − 8))]
- slope = [( − 7)/( − 4)]

slope = [7/4]

Find the value of x so that the line passing through the points (x, − 6) and ( − 13, − 4) has a slope of − 1.5

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - − [3/2] = [( − 4 − ( − 6))/( − 13 − x)]
- − [3/2] = [2/( − 13 − x)]
- 2(2) = − 3( − 13 − x)
- 4 = 39 + 3x
- 4 − 39 = 39 + 3x − 39
- − 35 = 3x

- [35/3] = x

Find the value of y so that the line passing through the points (4,y) and ( − 2, 5) has a slope of 2

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - 2 = [(5 − y)/( − 2 − 4)]
- 2 = [(5 − y)/( − 6)]
- 2( − 6) = 5 − y
- − 12 = 5 − y
- − 12 − 5 = 5 − y − 5
- − 17 = − y

17 = y

Find the value of y so that the line passing through the points ( − 6,y) and (3, − 1) has a slope of − 0.5

- slope = [(y
_{2}− y_{1})/(x_{2}− x_{1})] - − [1/2] = [( − 1 − y)/(3 − ( − 6))]
- − [1/2] = [( − 1 − y)/9]
- − 1(9) = 2( − 1 − y)
- − 9 = − 2 − 2y
- − 9 + 2 = − 2 − 2y + 2
- − 7 = − 2y

y = [7/2]

Determine the slope from the graph

- Use two points along the line to find the slope
- (Points can vary along the line)

slope = [(y

_{2}− y_{1})/(x_{2}− x_{1})] = [(3 − 0)/(1 − 0)] = 3Determine the slope from the graph

- Use two points along the line to find the slope
- (Points can vary along the line)

slope = [(y

_{2}− y_{1})/(x_{2}− x_{1})] = [(3 − 0)/(0 − ( − 18 ))] = − [1/6]Determine the slope from the graph

- Use two points along the line to find the slope
- (Points can vary along the line)

slope = [(y

_{2}− y_{1})/(x_{2}− x_{1})] = [(3 − 0)/(0 − ( − [3/4] ))] = 4Determine the slope from the graph

- Use two points along the line to find the slope
- (Points can vary along the line)

slope = [(y

_{2}− y_{1})/(x_{2}− x_{1})] = [(25 − 0)/(0 − ( − 75))] = [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.

Answer

### Slope and Rate of Change

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
- Rate of Change 0:06
- Other Words
- Example
- Slope 2:12
- Two Points
- Steepness of a Line
- Possible Slopes 4:29
- Positive Slope
- Negative Slope
- Zero Slope (Horizontal Line)
- Undefined Slope (Vertical Line)
- Example 1: Rate of Change of Table 8:19
- Example 2: Slope Through Points 10:52
- Example 3: Increasing/Decreasing 13:06
- Example 4: Slope Through Points 16:02

0 answers

Post by Yadira Perez on June 6, 2013

whydoesthisvideoshavesomanyerrors

1 answer

Last reply by: Dr Carleen Eaton

Sat Sep 1, 2012 2:20 PM

Post by Nagayasu Toshitatsu on August 28, 2012

For the last example, I believe that when you look for a, you can:

-6/5=-6/-7-a

because the numerator is equal, you can just make the denominator equal.

5=-7-a

5+a=-7-a+a

5+a-5=-7-5

a=-12

This equation will be correct.

I believe this is easier.