Question

find the slope of the line. what does the slope tell you about the speed of the car? the slope is \boxed{?}. the speed of the car is \boxed{?} miles per hour.

Explanation:

Step1: Identify two points on the line

The line passes through the origin \((0,0)\) and another point, say \((4, 80)\) (by looking at the graph, when time \(x = 4\) hours, distance \(y = 80\) miles).

Step2: Use the slope formula

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Substituting \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(4,80)\), we get \(m=\frac{80 - 0}{4 - 0}=\frac{80}{4}=20\).

Step3: Interpret the slope

The slope represents the rate of change of distance with respect to time, which is speed. So the slope (20) tells us the car's speed is 20 miles per hour.

Answer:

The slope is \(20\). The speed of the car is \(20\) miles per hour.