Question

1. todd is going to order custom shirts for his math team. he will pay for an initial design fee as well as the printing cost for each shirt.
2. this situation can be modeled as a linear relationship.

chart: x-axis shirts ordered (0 - 20), y-axis total cost ($) (20 - 200). line passes through (0, 40) and (20, 200).

1. what does the y-intercept of the line tell you about the situation?
2. todd will purchase 40 shirts.

the total cost of the order will be $200 if todd purchases 20 shirts.
after the design fee, each shirt will cost $8 to print.
the design fee is $40.

Explanation:

Step1: Understand y - intercept meaning

In a linear model \(y = mx + b\) for cost (\(y\)) vs. number of shirts (\(x\)), the \(y\)-intercept (\(b\)) is the value when \(x = 0\) (no shirts ordered).

Step2: Analyze the graph's y - intercept

From the graph, when \(x = 0\) (shirts ordered = 0), the \(y\)-value (cost) is \(\$40\). This represents the cost when no shirts are printed, which is the initial design fee.

Step3: Evaluate the options

• "Todd will purchase 40 shirts": The \(y\)-intercept has nothing to do with the number of shirts he purchases (that's about \(x\)-values, not \(y\)-intercept).
• "The total cost of the order will be \$200 if Todd purchases 20 shirts": This is about a point on the line (\(x = 20,y = 200\)), not the \(y\)-intercept.
• "After the design fee, each shirt will cost \$8 to print": This is about the slope (rate of change), not the \(y\)-intercept.
• "The design fee is \$40": Matches the \(y\)-intercept interpretation (cost when \(x = 0\) is the design fee).

Answer:

The design fee is \$40.