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 away from 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 2 miles per minute. tracies bus travels towards her home at an average speed of $\frac{1}{2}$ mile per minute.

Explanation:

Step1: Calculate the slope

The formula for slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((0,9)\) and \((8,5)\) from the graph.

$$m=\frac{5 - 9}{8 - 0}=\frac{-4}{8}=-\frac{1}{2}$$

The negative sign indicates that the distance from home is decreasing (bus is moving towards home). The magnitude \(\frac{1}{2}\) represents the rate of change of distance with respect to time.

Answer:

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