Question

distance remai
4
3
2
1
4 8 12 16 20 24 28 32 36 40
time spent running (minutes)
what does the y-intercept of the line tell you about the situation?
justine finished the race in 40 minutes.
when justine started the race, she was 10 kilometers from the finish line.
after running for 20 minutes, justine was 6 kilometers from the finish line.
justine ran 4 kilometers every 20 minutes.

Explanation:

Step1: Recall y - intercept definition

The y - intercept of a line is the value of \(y\) when \(x = 0\). In this context, \(x\) represents time spent running (in minutes) and \(y\) represents distance remaining (in kilometers). So when \(x=0\) (at the start of the race, time spent running is 0 minutes), the \(y\) - value is the distance from the finish line at the start.

Step2: Analyze each option

• Option 1: "Justine finished the race in 40 minutes" refers to when \(y = 0\) (distance remaining is 0), which is the x - intercept, not y - intercept.
• Option 2: "When Justine started the race, she was 10 kilometers from the finish line" - At \(x = 0\) (start time), we look at the y - intercept. From the graph, when \(x = 0\), we can infer (by extending the line or analyzing the slope - intercept form conceptually) that the y - intercept is 10 (since the line's equation can be thought of as \(y=mx + b\), where \(b\) is y - intercept. The slope \(m=\frac{\Delta y}{\Delta x}\), from the graph, when \(x = 40\), \(y = 2\)? Wait, no, let's re - check. Wait, actually, let's see the options. The second option says at start (\(x = 0\)) distance is 10 km from finish, which matches the y - intercept definition (y - value when \(x = 0\) is the initial distance from finish).
• Option 3: "After running for 20 minutes, Justine was 6 kilometers from the finish line" is a point on the line (\(x = 20,y = 6\)), not the y - intercept.
• Option 4: "Justine ran 4 kilometers every 20 minutes" refers to the slope (rate of change of distance with respect to time), not the y - intercept.

Answer:

When Justine started the race, she was 10 kilometers from the finish line.