tracie rides the bus home from school each day. the graph represents her distance from home relative to the…

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.

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.

Answer

Explanation:

Step1: Recall slope - speed relationship

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

Step2: Calculate the slope

The graph starts at (0, 9) and ends at (10, 4). The slope formula is $m=\frac{y_2 - y_1}{x_2 - x_1}$. Here, $y_1 = 9$, $y_2=4$, $x_1 = 0$, $x_2 = 10$. So $m=\frac{4 - 9}{10-0}=\frac{- 5}{10}=-\frac{1}{2}$. The negative sign indicates the distance from home is decreasing, meaning the bus is moving towards home and the magnitude of the slope $\frac{1}{2}$ represents the speed in miles per minute.

Answer:

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