Question

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Explanation:

Step1: Identify two points on the line

From the graph, we can see that when \( t = 0 \) (time in hours), the distance from home \( d = 300 \) miles (assuming the y - intercept is 300, looking at the grid: at \( x = 0 \), \( y \) is 300). When \( t=9 \) hours, \( d = 0 \) miles. So the two points are \( (0, 300) \) and \( (9, 0) \).

Step2: Use the slope formula

The slope \( m \) of a line passing through two points \( (x_1,y_1) \) and \( (x_2,y_2) \) is given by \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Here, \( x_1 = 0,y_1 = 300,x_2=9,y_2 = 0 \). So \( m=\frac{0 - 300}{9-0}=\frac{- 300}{9}\approx - 33.3 \). The rate of change is the slope, and since the distance from home is decreasing over time, the rate of change is - 33.3 miles per hour (which means the distance from home decreases by approximately 33.3 miles every hour, or equivalently, decreases by 300 miles every 9 hours as in option D).

Answer:

• 33.3 miles per hour (or \(\frac{-300}{9}\approx - 33.3\) miles per hour, the rate of change is - 33.3 miles per hour, indicating the distance from home decreases by about 33.3 miles every hour)