Question

Frank is riding his bike. The distance he travels varies directly with the number of revolutions (turns) his wheels make. See the graph below.
y
4
8
12
16
20
24
28
32
x
2
4
6
8
10
12
14
16
0
Distancetraveled(feet)
Numberofrevolutions

(a) How many revolutions does Frank make per foot of distance traveled?
revolution(s)
(b) What is the slope of the graph?

Answer 1

To answer the questions, we first need to interpret the graph based on the information provided. The graph shows the relationship between the number of revolutions Frank's wheels make (x-axis) and the distance traveled in feet (y-axis).

(a) To find how many revolutions Frank makes per foot of distance traveled, we can determine the ratio of distance traveled to the number of revolutions.

Looking at the graph:
- At \( x = 2 \) revolutions, \( y = 8 \) feet
- At \( x = 4 \) revolutions, \( y = 16 \) feet
- At \( x = 8 \) revolutions, \( y = 32 \) feet

We can use any of these points to determine the ratio:

From the point \( (2, 8) \):
\[
\text{Revolutions per foot} = \frac{2 \text{ revolutions}}{8 \text{ feet}} = \frac{1}{4} \text{ revolutions per foot}
\]

So, Frank makes **0.25 revolutions per foot of distance traveled.**

(b) The slope of the graph is the change in distance traveled (y) divided by the change in the number of revolutions (x). Using two points, we can calculate the slope.

Using the points \( (2, 8) \) and \( (4, 16) \):
\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{16 - 8}{4 - 2} = \frac{8}{2} = 4
\]

The slope of the graph is **4 feet per revolution.**

In summary:
(a) Frank makes **0.25 revolutions per foot of distance traveled.**
(b) The slope of the graph is **4 feet per revolution.**