5.1.3 Rate of Change and Slope Key Objectives
• Find rates of change from tables. • Find rates of change from graphs. • Find slopes from graphs, including horizontal and vertical lines. • Describe slopes. Key Terms • Rate of change is a ratio that compares the amount of change in the dependent variable to the amount of change in the independent variable. • The slope of a line is a measure of its steepness and is the ratio of rise to run.
• Rise is the difference in the y -values of two points on a line. • Run is the difference in the x -values of two points on a line.
Example 1 Consumer Application To find a rate of change, divide the change in the dependent variable by the change in the independent variable. In Example 1, Prof. Burger finds the rate of change for several time intervals and then compares these rates to determine which is greatest. In this example, the number of years is the independent variable and the cost is the dependent variable.
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