Question

Jessica is riding her bike. The number of revolutions (turns) her wheels make varies directly with the distance she travels. See the graph below.
y
2
4
6
8
10
12
14
16
x
8
16
24
32
40
48
56
64
0
Numberofrevolutions
Distancetraveled(feet)

(a) How far does Jessica travel per revolution?
feet
(b) What is the slope of the graph?

Answer 1

To find the answers to your questions:

(a) To determine how far Jessica travels per revolution, we can look at the data points on the graph. The number of revolutions (y-axis) is plotted against the distance traveled (x-axis). If we take any two points from the graph, we can calculate the distance traveled per revolution.

The slope of the line represents the distance traveled per revolution.

Using the values from the graph:
- When \(x = 8\), \(y = 1\)
- When \(x = 64\), \(y = 8\)

Now, we can calculate the slope:
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8 - 1}{64 - 8} = \frac{7}{56} = \frac{1}{8}
\]

This means that for every revolution, Jessica travels \(8\) feet.

(b) The slope of the graph, as calculated above, is \( \frac{1}{8} \) revolutions per foot, meaning Jessica makes \(1\) revolution for every \(8\) feet she travels.

Thus the answers are:
(a) 8 feet
(b) The slope of the graph is \( \frac{1}{8} \) revolutions per foot.