Question

after crossing a bridge, david drives at a constant speed. the graph below shows the distance (in miles) versus the time since he crossed the bridge (in hours). use the graph to answer the questions.
(a) what is the slope of the line?
(b) how much does the distance increase for each hour since david crossed the bridge?
\boxed{} miles

Explanation:

Step1: Recall the slope formula

The slope \( m \) of a line passing through two points \((x_1, y_1)\) and \((x_2, y_2)\) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). From the graph, we can see that the line passes through the origin \((0,0)\) and another point, say \((4, 240)\) (by looking at the graph, when \( x = 4 \) hours, \( y = 240 \) miles).

Step2: Calculate the slope

Using the two points \((0,0)\) and \((4, 240)\), we substitute into the slope formula: \( m=\frac{240 - 0}{4 - 0}=\frac{240}{4} = 60 \).

Step3: Interpret the slope for part (b)

The slope of a distance - time graph represents the speed (rate of change of distance with respect to time). So, the distance increases by the value of the slope for each hour. Since the slope is 60, the distance increases by 60 miles each hour.

Answer:

(a) The slope of the line is \(\boldsymbol{60}\).
(b) The distance increases by \(\boldsymbol{60}\) miles for each hour since David crossed the bridge.