Question

making sense of slope - item 32533
the graph shows the motion of a car driving on a highway.
enter a value to complete the statement.
car as speed is miles per hour.

Explanation:

Step1: Recall the formula for speed

Speed \(v=\frac{\text{Distance}}{\text{Time}}\). In a distance - time graph, the slope of the line gives the speed. The formula for the slope \(m\) of a line passing through two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m = \frac{y_2 - y_1}{x_2 - x_1}\).

Step2: Identify two points on the line for Car A

Let's take two points \((0,0)\) (when \(x = 0\) (time \(t = 0\) hours), \(y=0\) (distance \(d = 0\) miles)) and \((1.5,120)\) (when \(t = 1.5\) hours, \(d = 120\) miles).

Step3: Calculate the slope (speed)

Using the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\), substitute \(x_1 = 0,y_1 = 0,x_2=1.5,y_2 = 120\). Then \(m=\frac{120 - 0}{1.5-0}\).

$$m=\frac{120}{1.5}=80$$

Answer:

\(80\)