Answer
(a) $d(t) = 0.8t$
(b) Image below.
(c) 48 mi/h
Work Step by Step
(a) Linear function: $d(t) = at + b$
Since she starts in Detroit, and we start counting the time there. (t =0 and d(t) = 0). $b=0$
$d(t) = at$
Substituting the values:
$$40 = a(50) \longrightarrow a = \frac{40}{50} = 0.8$$
$$d(t) = 0.8t$$
(b) We already have 2 points (0,0) and (50,40). Plot these points, and draw the line that passes through both.
(c) speed = slope = a = 0.8
But 0.8 represents the speed in (mi/min). Since $1 \space h = 60 \space min$
$$0.8 \frac{mi}{min} \times \frac{60 \space min}{1 \space h} = 48 \space mi/h$$