A coordinate grid showing Number of T-Shirts on the horizontal x-axis and Total Cost in dollars on the vertical y-axis with 2 lines. The first line is labeled Shirt Box and posses through (0, 30) and the point at (4, 60). The second line is labeled Just Tees and passes through (0, 0) and the point at (6, 63).

Question

The volleyball team at West View High School is comparing T-shirt companies where they can purchase their practice shirts. The graph represents the two companies’ prices. What is the linear equation that represents each T-shirt company?

Shirt Box:

Just Tees:

Answer 1

To find the linear equations for both T-shirt companies, we need to use the slope-intercept form of a linear equation, which is:

\[ y = mx + b \]

where:

• \( y \) is the total cost,
• \( m \) is the slope,
• \( x \) is the number of T-shirts,
• \( b \) is the y-intercept (the total cost when \( x = 0 \)).

1. Shirt Box

Points:

• The line passes through the points (0, 30) and (4, 60).

Finding the slope (m): The slope \( m \) is calculated using the formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Using the points (0, 30) as \((x_1, y_1)\) and (4, 60) as \((x_2, y_2)\):

\[ m = \frac{60 - 30}{4 - 0} = \frac{30}{4} = 7.5 \]

Finding the y-intercept (b): From the point (0, 30), we see that the y-intercept \( b = 30 \).

Equation for Shirt Box: \[ y = 7.5x + 30 \]

2. Just Tees

Points:

• The line passes through the points (0, 0) and (6, 63).

Finding the slope (m): Using the points (0, 0) as \((x_1, y_1)\) and (6, 63) as \((x_2, y_2)\):

\[ m = \frac{63 - 0}{6 - 0} = \frac{63}{6} = 10.5 \]

Finding the y-intercept (b): From the point (0, 0), we see that the y-intercept \( b = 0 \).

Equation for Just Tees: \[ y = 10.5x + 0 \] or simply \[ y = 10.5x \]

Summary of Linear Equations

• Shirt Box: \( y = 7.5x + 30 \)
• Just Tees: \( y = 10.5x \)