Question

what does the slope of the line tell you about the situation? jackson has 6 laps to go 4 minutes after the race starts. jackson has 5 laps to go 6 minutes after the race starts. jackson completes 2 laps every minute. jackson completes 1 lap every 2 minutes.

Explanation:

Step1: Identify two points on the line

From the graph, when \( x = 0 \) (time = 0 minutes), \( y = 8 \) (laps remaining). When \( x = 2 \) (time = 2 minutes), \( y = 7 \) (laps remaining). Another point: when \( x = 4 \), \( y = 6 \); \( x = 8 \), \( y = 4 \).

Step2: Calculate the slope

The slope formula is \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Let's take \( (0, 8) \) and \( (2, 7) \). Then \( m=\frac{7 - 8}{2 - 0}=\frac{- 1}{2}=-0.5 \). The negative sign indicates a decrease in laps remaining over time. The absolute value \( 0.5=\frac{1}{2} \) means for every 2 minutes (increase in \( x \)), the laps remaining decrease by 1, which implies Jackson completes 1 lap every 2 minutes.

Step3: Analyze the options

• "Jackson has 6 laps to go 4 minutes after the race starts." This is a point on the line, not the slope's meaning.
• "Jackson has 5 laps to go 6 minutes after the race starts." This is a point on the line, not the slope's meaning.
• "Jackson completes 2 laps every minute." The slope calculation shows 0.5 laps per minute (or 1 lap every 2 minutes), so this is wrong.
• "Jackson completes 1 lap every 2 minutes." Matches the slope interpretation (since slope is -1/2, meaning 1 lap decrease every 2 minutes, so 1 lap completed every 2 minutes).

Answer:

Jackson completes 1 lap every 2 minutes.