Answer
$y=8.5n+25$
Work Step by Step
Let $n$ be the number of shirts and $y$ be the corresponding amount of shirts. A linear equation that gives the cost, $y$, for $n$ shirts takes the form of
$$
y=mn+b,
$$
where $m$ is the slope and $b$ is the $y$-intercept.
Since $10$ shirts cost \$$110$, this can be represented by the ordered pair $(n_1,y_1)=(10,110)$. Since $30$ shirts cost \$$280$, this can be represented by the ordered pair $(n_2,y_2)=(30,280)$.
The formula for finding the slope, $m$, of the line passing through two points, $(n_1,y_1)$ and $(n_2,y_2)$ is given by $m=\frac{y_1-y_2}{n_1-n_2}$. That is,
$$\begin{aligned}
m&=\frac{y_1-y_2}{n_1-n_2}
\\&=
\frac{110-280}{10-30}
\\&=
\frac{-170}{-20}
\\&=
8.5
.\end{aligned}
$$
With $m=8.5$, the linear equation that gives the cost, $y$, for $n$ shirts takes the form of
$$
y=8.5n+b
.$$
Since the line passes through the point $(10,110)$, substitute $n=10$ and $y=110$ in the equation above to solve for $b$. That is,
$$\begin{aligned}
y&=8.5n+b
\\
110&=8.5(10)+b
\\
110&=85+b
\\
110-85&=b
\\
b&=25
.\end{aligned}
$$
With $b=25$, then the linear equation that gives the cost for $n$ shirts is $y=8.5n+25$.
