The distance a baseball travels when a player hits the ball varies directly with the speed with which the player swings the bat. The graph below shows the distances a baseball travels (in feet) and the speed of the swing (in miles per hour).

Question

A graph titled Baseball Speed has speed of swing (in miles per hour) on the x-axis, and distance (in feet) on the y-axis. A line goes through points (0, 0), (40, 200), (60, 300).

Based on the graph, which relationship exists between the speed of the swing and the distance the ball travels?
The distance is 0.1 times the swing speed.
The distance is 0.2 times the swing speed.
The distance is 5 times the swing speed.
The distance is 10 times the swing speed.

Answer 1

To determine the relationship between the speed of the swing and the distance the ball travels based on the graph, we can look at the coordinates of the points given.

From the graph, we can see the following points:

1. (0, 0)
2. (40, 200)
3. (60, 300)

We can use these points to find the ratio of distance to speed.

Let's calculate the ratios for the two non-origin points:

• For the point (40, 200): \[ \frac{\text{Distance}}{\text{Speed}} = \frac{200 \text{ feet}}{40 \text{ mph}} = 5 \text{ feet per mph} \]

• For the point (60, 300): \[ \frac{\text{Distance}}{\text{Speed}} = \frac{300 \text{ feet}}{60 \text{ mph}} = 5 \text{ feet per mph} \]

Both points yield the same ratio of \(5\) feet of distance for every \(1\) mph of speed.

From the calculations, we can conclude that the distance the baseball travels is \(5\) times the swing speed.

Thus, the correct relationship is: The distance is 5 times the swing speed.