To determine how far Jina travels per revolution and the slope of the graph, we can analyze the relationship between the distance traveled and the number of revolutions based on the provided data points.
(a) How far does Jina travel per revolution?
From the graph, we can see that as the number of revolutions (x) increases, the distance traveled (y) also increases. To find the distance per revolution, we can select two points from the graph. For example, using the points (2, 4) and (10, 20):
- For 2 revolutions, she travels 4 feet.
- For 10 revolutions, she travels 20 feet.
To find how far Jina travels per revolution, calculate the distance per revolution from one of the points:
\[ \text{Distance per revolution} = \frac{y}{x} \]
Using the point (2, 4): \[ \text{Distance per revolution} = \frac{4 \text{ feet}}{2 \text{ revolutions}} = 2 \text{ feet/revolution} \]
Thus, Jina travels 2 feet per revolution.
(b) What is the slope of the graph?
The slope of a graph in a direct variation context (where distance varies directly with revolutions) is the same as the distance traveled per revolution. Using the same points, we can find the slope \(m\) using the formula:
\[ m = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1} \]
Using points (2, 4) and (10, 20): \[ m = \frac{20 - 4}{10 - 2} = \frac{16}{8} = 2 \]
Thus, the slope of the graph is 2 (feet per revolution).
Final Answers:
(a) 2 feet per revolution
(b) Slope = 2