Question

tread
0.2
0.15
0.1
0.05
1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000
distance driven (miles)
what does the y-intercept of the line tell you about the situation?
if ed drives 10,000 miles, the tread depth will be 0.2 inches.
the tread depth will decrease 0.3 inches every 10,000 miles ed drives.
when ed buys the tires, the tread depth is 0.3 inches.
the tread depth will decrease 0.1 inches every 10,000 miles ed drives.

Explanation:

Step1: Recall y-intercept definition

The y - intercept of a line \(y = mx + b\) is the value of \(y\) when \(x = 0\). In this context, \(x\) is the distance driven (in miles) and \(y\) is the tread depth (in inches). So when \(x = 0\) (distance driven is 0 miles, i.e., when Ed buys the tires), the y - intercept gives the tread depth at that time.

Step2: Analyze each option

• Option 1: "If Ed drives 10,000 miles, the tread depth will be 0.2 inches." This is about \(x = 10000\), not the y - intercept (\(x = 0\)), so it's incorrect.
• Option 2: "The tread depth will decrease 0.3 inches every 10,000 miles Ed drives." This is about the slope (rate of change), not the y - intercept, so it's incorrect.
• Option 3: "When Ed buys the tires, the tread depth is 0.3 inches." When Ed buys the tires, he has driven 0 miles (\(x = 0\)). The y - intercept is the tread depth at \(x = 0\). From the graph, if we extend the line, when \(x = 0\), the tread depth should be 0.3 (since at \(x = 10000\), it's around 0.2, so the y - intercept is higher). This matches the definition of y - intercept.
• Option 4: "The tread depth will decrease 0.1 inches every 10,000 miles Ed drives." This is about the slope, not the y - intercept, so it's incorrect.

Answer:

When Ed buys the tires, the tread depth is 0.3 inches.