Question

writing equations to represent equations
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:
(graph description: a coordinate graph with x - axis labeled number of t - shirts (ranging from 0 to 16) and y - axis labeled total cost ($) (ranging from 0 to 100). two lines: shirt box (blue) passing through (4, 60) and having a y - intercept around 30?; just tees (orange) passing through (6, 63) and the origin (0,0).)

Explanation:

Step1: Find equation for Shirt Box

We use the slope - intercept form of a linear equation $y = mx + b$, where $m$ is the slope and $b$ is the y - intercept.
From the graph, when $x = 0$, the y - intercept $b$ for Shirt Box is 30 (since the line starts at $(0,30)$).
We have a point $(4,60)$ on the line for Shirt Box. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,30)$ and $(x_2,y_2)=(4,60)$. Then $m=\frac{60 - 30}{4 - 0}=\frac{30}{4}=7.5$ or $\frac{15}{2}$.
Using $y=mx + b$, with $m = 7.5$ and $b = 30$, the equation is $y=7.5x + 30$ or $y=\frac{15}{2}x+30$.

Step2: Find equation for Just Tees

For Just Tees, the line passes through the origin $(0,0)$, so the y - intercept $b = 0$.
We have a point $(6,63)$ on the line. The slope $m=\frac{y_2 - y_1}{x_2 - x_1}$. Let $(x_1,y_1)=(0,0)$ and $(x_2,y_2)=(6,63)$. Then $m=\frac{63 - 0}{6 - 0}=10.5$ or $\frac{21}{2}$.
Using $y = mx + b$ with $m=10.5$ and $b = 0$, the equation is $y = 10.5x$ or $y=\frac{21}{2}x$.

Answer:

Shirt Box: $y = 7.5x+30$ (or $y=\frac{15}{2}x + 30$)
Just Tees: $y=10.5x$ (or $y=\frac{21}{2}x$)