Question

derek is renting a van from abby’s autos. he will be charged an initial fee to rent the van and an additional amount that depends on how far he drives it. this situation can be modeled as a linear relationship. chart: x-axis: distance driven (miles), y-axis: total cost ($); line with y-intercept at $50 what does the y-intercept of the line tell you about the situation? options: including the initial fee, derek will pay $70 to rent the van and drive 100 miles. after the initial fee, derek will pay $0.20 per mile he drives. the initial fee is $50. derek will drive the van for 200 miles.

Explanation:

Step1: Understand y - intercept meaning

In a linear relationship \(y = mx + b\) (where \(y\) is total cost, \(x\) is distance, \(m\) is slope, \(b\) is y - intercept), the y - intercept (\(b\)) occurs when \(x = 0\).

Step2: Analyze the graph's y - intercept

From the graph, when \(x = 0\) (distance driven is 0 miles), the \(y\) - value (total cost) is \(\$50\). This means when Derek drives 0 miles (just the initial fee to rent the van), the cost is \(\$50\). So the y - intercept represents the initial fee.

Step3: Evaluate the options

• "Including the initial fee, Derek will pay $70 to rent the van and drive 100 miles": This is about a point on the line (\(x = 100,y = 70\)), not the y - intercept.
• "After the initial fee, Derek will pay $0.20 per mile he drives": This is about the slope (rate per mile), not the y - intercept.
• "The initial fee is $50": This matches the y - intercept interpretation (when \(x = 0\), cost is \(50\)).
• "Derek will drive the van for 200 miles": The y - intercept has nothing to do with the total distance driven, it's about cost at 0 distance.

Answer:

The initial fee is $50