What is the unit rate depicted in the graph?

On a coordinate plane, a graph titled Lap Times has minutes on the x-axis and Laps on the y-axis. A line goes through points (4, 3) and (8, 6).
0.75 laps in one minute
1.25 laps in one minute
3 laps in 4 minutes
4 laps in 3 minutes

1 answer

To find the unit rate depicted in the graph, we can analyze the points given: (4, 3) and (8, 6). These points represent the relationship between the minutes (x-axis) and laps (y-axis).

First, we can find the slope of the line between these two points. The formula for the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting in the values from the points (4, 3) and (8, 6):

\[ m = \frac{6 - 3}{8 - 4} = \frac{3}{4} \]

The slope, which is the unit rate of laps per minute, is \( \frac{3}{4} \). This means for every 1 minute, there are \( \frac{3}{4} \) laps completed.

To express this as a unit rate in terms of laps per minute:

  • \( \frac{3}{4} \) laps in one minute is equivalent to 0.75 laps in one minute.

Thus, the correct answer is:

0.75 laps in one minute.