A coordinate plane with a straight line with a positive slope starting at (0, 0) and passing through the points (1.0, 10) and (2.0, 20).

Use the graph to find the slope.

slope = slope equals StartFraction rise Over run EndFraction.



The runner’s speed is
minutes per mile.

User Icon for Bot GPT-4o Bot GPT-4o answered
3 months ago

Let's address the problem step-by-step.

To find the slope of the straight line on a coordinate plane, you can use the formula for the slope (m), which is given by:

\[ m = \frac{{\text{rise}}}{{\text{run}}} \]

Given points through which the line passes: (0,0), (1,10), and (2,20).

Choose any two points to calculate the slope. Here, we'll use (0,0) and (1,10).

1. Determine the rise (change in y-values):
\[ \text{Rise} = y_2 - y_1 = 10 - 0 = 10 \]

2. Determine the run (change in x-values):
\[ \text{Run} = x_2 - x_1 = 1 - 0 = 1 \]

3. Plug these values into the slope formula:
\[ m = \frac{{\text{rise}}}{{\text{run}}} = \frac{10}{1} = 10 \]

So, the slope of the line is 10.

The slope of the line represents the rate of change of y with respect to x. In this context, if the y-axis represents distance and the x-axis represents time, then the slope represents the speed.

To interpret this in terms of speed:
- The runner's speed is 10 units per 1 unit of time.

Given that the slope reflects the change in distance (y) per change in time (x), we can conclude that the runner's speed is **10 miles per minute**.

Let's clarify this conversion if necessary, but based on the given slope using the rise and run from the points provided:

\[ \text{Runner's speed} = 10 \text{ miles per minute} \]

Remember to check the units of the x and y-axis to be certain, but given the description, this interpretation is correct.