Chapter 6: Linear Equations & Their Graphs

6.1Rate of Change and Slope

Vocabulary

• Rate:– A comparison of two quantities measured in

different units• Rate of change:– Allows you to see the relationship between two

quantities that are changing

Change in the dependent variableChange in the independent variable

Example 1

• For the data, is the rate of change for each pair of consecutive days the same? What does the rate of change represent?

Cost of Renting a Computer

# of days Rental Charge

1 $60

2 $75

3 $90

4 $105

5 $120

Example 1a

• Does finding the rate of change for just one pair of days mean that the rate of change is the same for all data?

Rate of Change

• If data is linear, you can use a graph to find a rate of change

vertical change (change in dependent variable)Horizontal change (change in independent variable)

Example 2• The graph shows the altitude of an airplane as it

comes in for a landing. Find the rate of change. Explain what this rate of change means.

Example 2a

• Find the rate of change of the data in the graph:

Slope

• The rate of change of a line

• Think of the slope of roads, roofs, etc.

• Steeper slope = larger number

Example 3a

• Find the slope of the line:

Example 3b

• Find the slope of the line:

Slope

xy

xxyy

runrisem

12

12

Example 4

• Find the slope of the line through A(-2,1) and B(6,7).

Example 4a

• Find the slope of the line through C(2,5) and D(4,7).

Example 4b

• Find the slope of the line through P(-1,4) and Q(3,-2).

Example 4c

• Find the slope of the line through M(a,b) and N(c,d)

Example 5

• Find the slope of the line:

Example 5a

• Find the slope of the line:

Example 5b

• Find the slope of the line:

Example 5c

• Find the slope of the line:

Summary

• Positive Slope

• Negative Slope

• Zero Slope

• No Slope

Homework

• P. 312

• 2-26 even, 30-35 all