Question

the slope of a graph. find the slope of the graph and the unit r

1. scott hiking

distance (mi)
10
5
0
5
10
time (h)
slope = \frac{rise}{run}=
unit rate = mi/h

Explanation:

Step1: Identify two points on the line

We can use the points (0,0) and (10,5) from the graph.

Step2: Calculate the rise and run

The rise is the change in the y - values. For points (0,0) and (10,5), the rise from (0,0) to (10,5) is \(y_2 - y_1=5 - 0 = 5\). The run is the change in the x - values, \(x_2 - x_1=10 - 0 = 10\).

Step3: Calculate the slope

Using the formula slope \(=\frac{\text{rise}}{\text{run}}\), we substitute the values of rise and run. So, slope \(=\frac{5}{10}=\frac{1}{2}\).

Step4: Determine the unit rate

The unit rate is the same as the slope in this context of distance - time graph. The unit rate represents the distance per unit time. Since the slope is \(\frac{1}{2}\) and the units are miles per hour, the unit rate is \(\frac{1}{2}\) mi/h.

Answer:

slope \(=\frac{1}{2}\), unit rate \(=\frac{1}{2}\) mi/h