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:
- \( (2, 4) \)
- \( (4, 8) \)
- \( (6, 12) \)
- \( (8, 16) \)
- \( (10, 20) \)
- \( (12, 24) \)
- \( (14, 28) \)
- \( (16, 32) \)
- \( (18, 36) \)
(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.