Ellen makes and sells bookmarks. She graphs the number of bookmarks sold compared to the total money earned. What is the rate of change for the function graphed to the left?

Answer 1

To find the rate of change of the function graphed, which shows the number of bookmarks sold compared to the total money earned, you need to determine the slope of the line on the graph. The slope, or rate of change, represents how much money is earned per bookmark sold.

Here's a step-by-step method to find the rate of change:

1. **Identify Two Points on the Line**: Suppose you have two points on the graph \((x_1, y_1)\) and \((x_2, y_2)\), where \(x\) represents the number of bookmarks sold and \(y\) represents the total money earned.

2. **Calculate the Slope (Rate of Change)**:
The formula to calculate the slope \(m\) is:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
This formula gives the change in total money earned per change in the number of bookmarks sold.

3. **Plug in the Coordinates**: Substitute the coordinates of the two points you identified on the graph into the formula.

For instance, if you have two points (2, 10) and (5, 25):

- \( (x_1, y_1) = (2, 10) \)
- \( (x_2, y_2) = (5, 25) \)

The slope \( m \) would be calculated as follows:
\[
m = \frac{25 - 10}{5 - 2} = \frac{15}{3} = 5
\]

This means the rate of change is 5, which indicates that Ellen earns $5 per bookmark she sells.

In summary, the rate of change can be determined by finding the slope of the line on the graph created from the points showing the relationship between the number of bookmarks sold and the total money earned.