Answer
$(a)$ $S=3500t+60000$
$(b)$
The slope represents rate of change of her annual salary.
The $S$-intercept represents her salary before increase.
$(c)$ $\$102,000$
Work Step by Step
$(a)$ According to the information given, we can write:
$\$70500-\$60000=\$10500$
Her salary has increased by $\$10500$ within 3 years. If the salary increases linearly, the her salary increases by $\$\frac{10500}{3}=\$3500$ per year. So, we can write the relation:
$S=3500t+60000$
$(b)$
The slope represents rate of change of her annual salary.
The $S$-intercept represents her salary before increase.
$(c)$ $t=12$
$S=3500\times12+60000=\$102000$