Tell whether the slope is positive or negative. Then find the slope. Do Now Tell whether the slope is positive or negative. Then find the slope. Negative; -1

Homework p208 positive; 1 Negative; -1/2 11) negative; -3

Learn to determine the slope of a line and to recognize constant and variable rates of change.

A rate of change is a rate that describes how one quantity changes in relation to another. A constant rate of change is the rate of change of a linear relationship

The ratio of two quantities that change, such as slope, is a rate of change. A constant rate of change describes changes of the same amount during equal intervals. It is displayed on graphs as linear (a line). A variable rate of change describes changes of a different amount during equal intervals. It is displayed on graphs as nonlinear (not a line).

rate of change constant rate of change Ratios and Proportional Relationships rate of change constant rate of change Course 2, Lesson 1-7

Example 1 Find the constant rate of change for the table. Students Number of textbooks 5 15 10 30 45 20 60 The change in the number of textbooks is 15. The change in the number of students is 5. c change in number of textbooks = 15 textbooks change in number of students 5 students = 3 textbooks 1 student Write as a unit rate So, the number of textbooks increased by 15 for every 5 students it rate.

Example C Tell whether each graph shows a constant or variable rate of change. A. B. The graph is nonlinear, so the rate of change is variable. The graph is linear, so the rate of change is constant.

Tell whether each graph shows a constant or variable rate of change. Example C continued Tell whether each graph shows a constant or variable rate of change. A. B. y y 4 4 2 2 x x –4 –2 2 4 –4 –2 2 4 –2 –2 –4 –4 The graph is linear, so the rate of change is constant. The graph is nonlinear, so the rate of change is variable.