To solve this problem, let's analyze the details given:

1. Price per T-shirt: $8.
2. Fixed shipping cost: $15.
3. Graph: It shows the total cost (y-axis) based on the number of T-shirts (x-axis).

Setting Up the Equation

This scenario represents a linear relationship between the total cost ($y$) and the number of T-shirts ($x$) bought. The cost function can be represented as: $y = mx + b$ where:

• $m$ is the cost per T-shirt ($8),
• $x$ is the number of T-shirts,
• $b$ is the fixed shipping cost ($15).

Plugging in Values

Given $m = 8$ and $b = 15$, the equation becomes: $y = 8x + 15$

Verifying with the Graph

Using this equation, the total cost increases by $8 for each additional T-shirt, starting from an initial cost of $15 when zero T-shirts are ordered. This matches the graph structure provided.

Answer

The equation that best represents the linear relationship is: $y = 8x + 15$

Would you like a more detailed explanation, or have any questions?

Here are some related questions for practice:

1. How would the equation change if the price per T-shirt increased to $10?
2. What would the total cost be if 10 T-shirts were ordered?
3. If the shipping cost were removed, what would the new equation be?
4. How does the slope of the line relate to the price per T-shirt?
5. How can you determine the fixed shipping cost from a graph?

Tip: In linear equations, the y-intercept often represents a fixed starting value, while the slope indicates the rate of change per unit.