Holt Algebra 1

5-3 Rate of Change and Slope

2 1.5 2 5 3 5 8g

Evaluate the functions for the given input values.

For f(x) = 3x + 2, find f(x) when x = 7 and when x = –4.

For g(t) = 1.5t – 5, find g(t) when t = 6 and when t = –2.

7 3 7 2 32 221f

4 3 4 2 12 12 0f

6 1.5 6 9 5 45g

Holt Algebra 1

5-3 Rate of Change and Slope

Find rates of change and slopes.

Relate a constant rate of change to the slope of a line.

Objectives

Holt Algebra 1

5-3 Rate of Change and Slope

A rate of change is a ratio that compares the amount of change in a dependent variable to the amount of change in an independent variable.

y

x

Holt Algebra 1

5-3 Rate of Change and SlopeThe table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

dependent: temperature independent: month

2 1

2 1

056 56 0

Rate of change3 2 1

y y

x x

0 degrees per month

Holt Algebra 1

5-3 Rate of Change and SlopeThe table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

dependent: temperature independent: month

2 1

2 1

3.563 56 7

Rate of Change5 3 2

y y

x x

3.5 degrees per month

Holt Algebra 1

5-3 Rate of Change and SlopeThe table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

dependent: temperature independent: month

2 1

2 1

471 63 8

Rate of Change7 5 2

y y

x x

4 degrees per month

Holt Algebra 1

5-3 Rate of Change and SlopeThe table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

dependent: temperature independent: month

2 1

2 1

172 71 1

Rate of Change8 7 1

y y

x x

1 degree per month

Holt Algebra 1

5-3 Rate of Change and SlopeThe table shows the average temperature (°F) for five months in a certain city. Find the rate of change for each time period. During which time period did the temperature increase at the fastest rate?

The temperature increased at the highest rate

between months 5 and 7.

Holt Algebra 1

5-3 Rate of Change and Slope

Graph the data from Example 1 and show the rates of change.

1 2 3 4 5 6 7 8

5055606570758085

x

T x

0

1

7

2

8

2

1

1

Holt Algebra 1

5-3 Rate of Change and Slope

If all of the connected segments have the same rate of change, then they all have the same steepness and together form a straight line. The constant rate of change of a line is called the slope of the line.

Holt Algebra 1

5-3 Rate of Change and SlopeFind the slope of the line.

(3, 2)

(–6, 5)

3

9

2 1

2 1

1

3

2 5 3

3 6 9

y ym

x x

Holt Algebra 1

5-3 Rate of Change and Slope

Find the slope of the line that contains (0, –3) and (5, –5).

x

y

2 1

2 1

5 23

5 0 5

y ym

x x

Holt Algebra 1

5-3 Rate of Change and Slope

Find the slope of each line.

A. B.

C. D.

Undefined

Undefined

0m

0m

Holt Algebra 1

5-3 Rate of Change and Slope

As shown in the previous examples, slope can be positive, negative, zero or undefined. You can tell which of these is the case by looking at a graph of a line–you do not need to calculate the slope.

Holt Algebra 1

5-3 Rate of Change and Slope

Tell whether the slope of each line is positive, negative, zero or undefined.

A. B.

C. D.

Positive

Undefined

Negative

Positive

Holt Algebra 1

5-3 Rate of Change and Slope

HW pp. 314-317/13-31 Odd, 34-41