Question

1. find the unit rate from this graph.

graph with miles on y - axis (8, 16, 24, 32) and hours on x - axis (2, 4, 6, 8), with points at (2,8), (4,16), (6,24), (8,32)

Explanation:

Step1: Identify two points

From the graph, we can take the point (2, 8) and (4, 16) (or any other two points). Let's use (2, 8) where \( x_1 = 2 \) (hours) and \( y_1 = 8 \) (miles), and (4, 16) where \( x_2 = 4 \) (hours) and \( y_2 = 16 \) (miles).

Step2: Calculate the slope (unit rate)

The formula for slope (unit rate, since it's miles per hour) is \( \text{slope} = \frac{y_2 - y_1}{x_2 - x_1} \). Plugging in the values: \( \frac{16 - 8}{4 - 2} = \frac{8}{2} = 4 \). We can also check with another point, like (6, 24): \( \frac{24 - 16}{6 - 4} = \frac{8}{2} = 4 \), or (8, 32): \( \frac{32 - 24}{8 - 6} = \frac{8}{2} = 4 \). So the unit rate is 4 miles per hour.

Answer:

4 miles per hour