Question

the image shows a graph with x - axis labeled hours, x and y - axis labeled y. the line passes through the origin (0,0) and another point. there are some text boxes with ? indicating missing information related to the line, such as the line is..., rate of change of the..., variable is....

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \) (hours), \( y = 0 \) (miles). When \( x = 2 \) (hours), \( y = 80 \) (miles).

Step2: Calculate the rate of change (slope)

The formula for the rate of change (slope) \( m \) is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((0,0)\) and \((2,80)\), we get \( m=\frac{80 - 0}{2 - 0}=\frac{80}{2}=40 \).

Answer:

The rate of change of the line (miles per hour) is 40.