Question

Jina is riding her bike. The distance she travels varies directly with the number of revolutions (turns) her wheels make. See the graph below.
y
4
8
12
16
20
24
28
32
36
x
2
4
6
8
10
12
14
16
18
0
Distancetraveled(feet)
Numberofrevolutions

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

Answer 1

To analyze the relationship between the distance traveled (y-axis) and the number of revolutions (x-axis), we will designate the distance traveled as \( y \) and the number of revolutions as \( x \).

### Given Data Points:
From the graph, we can observe the following points:
1. \( (2, 4) \)
2. \( (4, 8) \)
3. \( (6, 12) \)
4. \( (8, 16) \)
5. \( (10, 20) \)
6. \( (12, 24) \)
7. \( (14, 28) \)
8. \( (16, 32) \)
9. \( (18, 36) \)

### (a) How far does Jina travel per revolution?

The distance traveled varies directly with the number of revolutions, which means we can express this relationship with the equation:

\[ y = kx \]

Where \( k \) is the constant of proportionality (the distance traveled per revolution).

Using any of the points provided:
Let's take the point \( (2, 4) \):
\[ 4 = k \cdot 2 \]
\[ k = \frac{4}{2} = 2 \text{ feet per revolution} \]

Therefore, Jina travels **2 feet per revolution**.

### (b) What is the slope of the graph?

Since the relationship between the distance traveled and the number of revolutions is linear (the graph is a straight line), the slope of the graph is equal to the constant of proportionality \( k \).

From our calculation in part (a):

The slope (\( m \)) is:

\[ m = k = 2 \]

So, the slope of the graph is **2**.