Answer
a) $S=3500t+60,000$
b) Slope = annual increase; $S$-intercept = initial salary
c) $\$102,000$
Work Step by Step
a) The salary $S$ is a linear function of the variable time. $t$, where $t=0$ is the year when she is hired.
We are given:
$$\begin{align*}
S(0)&=60,000\\
S(3)&=70,500.
\end{align*}$$
First determine the slope $m$ of the line:
$$\begin{align*}
m&=\dfrac{70,500-60,000}{3-0}\\
&=\dfrac{10,500}{3}\\
&=3500.
\end{align*}$$
The equation of the line becomes:
$$S=3500t+b.$$
We are given the $S$-intercept $b=60,000$, so the equation of the line is:
$$\begin{align*}
S&=3500t+60,000.\tag1
\end{align*}$$
b) The slope $m=3500$ represents the annual increase of the salary.
The $S$-intercept is the value of the salary at the moment when she is hired.
c) We determine the salary after $12$ years by substituting $t=12$ in Eq. $(1)$:
$$S(12)=3500(12)+60,000=42,000+60,000=102,000.$$
