1. Rate of Change and Slope
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What is the rate of change between each pair of consecutive points?
Is the rate of change constant? Yes
Explanation: See solution.
We want to determine if the rate of change in cost is constant with respect to the number of pencils bought. To do so, we will calculate the rate of change between each consecutive pair of points. We will use the rate of change formula to find the rate of change r between two points.
r= y_2-y_1/x_2-x_1
Substitute ( 1,0.25) & ( 4,1)
Subtract terms
Use a calculator
The rate of change between the first two points is 0.25. We will use the same method to find the rate of change r between (4,1) and (7,1.75), and between (7,1.75) and (12,3).
| Pair of Points | y_2-y_1/x_2-x_1 | r=y_2-y_1/x_2-x_1 |
|---|---|---|
| ( 1,0.25) & ( 4,1) | 1- 0.25/4- 1 | 0.25 |
| ( 4,1) & ( 7,1.75) | 1.75- 1/7- 4 | 0.25 |
| ( 7,1.75) & ( 12,3) | 3- 1.75/12- 7 | 0.25 |
As shown, all the rates are the same. This means that the rate of change is constant.