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? tracie’s bus travels towards her home at an average speed of \\(\frac{1}{2}\\) mile per minute. tracie’s bus travels towards her home at an average speed of 2 miles per minute. tracie’s bus travels away from her home at an average speed of \\(\frac{1}{2}\\) mile per minute. tracie’s bus travels away from her home at an average speed of 2 miles per minute.

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \) (minutes since bus left school), \( y = 9 \) miles (distance from home). When \( x = 10 \), \( y = 4 \) miles.

Step2: Calculate the slope

Slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{4 - 9}{10 - 0}=\frac{-5}{10}=-\frac{1}{2} \). The negative sign means distance from home is decreasing (towards home), and the absolute value \( \frac{1}{2} \) is miles per minute.

Answer:

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