Question

A graph titled Runner's Speed has distance (miles) on the x-axis and Time (minutes) on the y-axis. A line goes through points (1, 10) and (2, 20).
Use the graph to find the slope.

slope = StartFraction rise Over run EndFraction

What is the runner’s speed?
minutes per mile

Answer 1

To find the slope of the line on the graph titled Runner's Speed, we can use the formula for slope, which is given by:

\[
\text{slope} = \frac{\text{rise}}{\text{run}} = \frac{y_2 - y_1}{x_2 - x_1}
\]

Here, we have two points on the graph: \( (1, 10) \) and \( (2, 20) \).

Let's define the points as follows:
- \( (x_1, y_1) = (1, 10) \)
- \( (x_2, y_2) = (2, 20) \)

Now, we can compute the rise and run:

1. **Rise**: \( y_2 - y_1 = 20 - 10 = 10 \)
2. **Run**: \( x_2 - x_1 = 2 - 1 = 1 \)

Now, substituting these values into the slope formula:

\[
\text{slope} = \frac{10}{1} = 10
\]

The slope of the graph is \( 10 \) minutes per mile.

Therefore, the runner’s speed is **10 minutes per mile**.