Question

tracie rides the bus home from school each day. the graph represents her distance from home relative to the number of minutes since the bus left the school. driving home what does the slope of the graph mean? tracies bus travels towards her home at an average speed of 1/2 mile per minute. tracies bus travels away from her home at an average speed of 1/2 mile per minute. tracies bus travels towards her home at an average speed of 2 miles per minute. tracies bus travels away from her home at an average speed of 2 miles per minute.

Explanation:

Step1: Recall slope - speed relationship

The slope of a distance - time graph represents speed. Here, the distance from home is decreasing as time increases, so the bus is moving towards home.

Step2: Calculate the slope

The initial distance from home is 9 miles and after 8 minutes, the distance is 5 miles. The change in distance $\Delta y=5 - 9=- 4$ miles and the change in time $\Delta x = 8$ minutes. The slope $m=\frac{\Delta y}{\Delta x}=\frac{5 - 9}{8}=\frac{-4}{8}=-\frac{1}{2}$ mile per minute. The negative sign just indicates the distance from home is decreasing. The magnitude of the slope represents the speed, which is $\frac{1}{2}$ mile per minute.

Answer:

Tracie's bus travels towards her home at an average speed of $\frac{1}{2}$ mile per minute.