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. what does the slope of the graph mean? tracies bus travels towards her home at an average speed of $\frac{1}{2}$ 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 $\frac{1}{2}$ mile per minute. tracies bus travels away from her home at an average speed of 2 miles per minute.

Explanation:

Step1: Recall the formula for slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). In a distance - time graph, slope represents speed. Here, the \(y\) - axis is distance from home (in miles) and the \(x\) - axis is time (in minutes).

Step2: Select two points on the line

Let's take the points \((0,9)\) and \((10,4)\).

Step3: Calculate the slope

Using the slope formula \(m=\frac{4 - 9}{10-0}=\frac{- 5}{10}=-\frac{1}{2}\). The negative sign indicates that the distance from home is decreasing (traveling towards home). The magnitude of the slope \(\frac{1}{2}\) represents the speed.

Answer:

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