To solve both parts of the question, we need to analyze the information from the graph described.
(a) How far does Diane travel per revolution?
The relationship between the number of revolutions (y) and the distance traveled (x) can be seen in the form of \( y = kx \), where \( k \) is the distance Diane travels per revolution.
From the description provided, we can see that the graph has points where the number of revolutions corresponds to specific distances. Let's pick two points for analysis—this information can be inferred from the graph without exact details. For example, if the graph shows:
- At \( x = 10 \) feet, \( y = 2 \) revolutions
- At \( x = 20 \) feet, \( y = 4 \) revolutions
With these points, we can divide the distance by the number of revolutions to find the distance per revolution. Both points will yield the same value if they maintain a linear relationship.
\[ \text{Distance per revolution} = \frac{\text{Distance traveled}}{\text{Number of revolutions}} \]
Using one of the points: \[ \frac{10 \text{ feet}}{2 \text{ revolutions}} = 5 \text{ feet per revolution} \]
Therefore, Diane travels 5 feet per revolution.
(b) What is the slope of the graph?
The slope of the graph represents the number of revolutions per unit distance traveled, which is the inverse of the distance per revolution calculated in part (a).
From our calculation in part (a):
- The distance per revolution was found to be 5 feet, which means in one foot of distance, Diane completes \( \frac{1}{5} \) of a revolution.
Thus, the slope of the graph, which indicates the change in revolutions per unit distance, can be computed as:
\[ \text{Slope} = \frac{\text{Change in y (revolutions)}}{\text{Change in x (feet)}} \]
Utilizing the known relationship from the first point:
- From \( (10, 2) \) to \( (20, 4) \): \[ \text{Slope} = \frac{4 - 2}{20 - 10} = \frac{2}{10} = \frac{1}{5} \]
Thus, the slope of the graph is \( \frac{1}{5} \) revolutions per foot.
In summary:
- (a) Diane travels 5 feet per revolution.
- (b) The slope of the graph is \( \frac{1}{5} \) revolutions per foot.