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).

Question

Use the graph to find the slope.

slope = slope equals StartFraction rise Over run EndFraction.



The runner’s speed is
minutes per mile.

Answer 1

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.