Answer
(a) $C(x) = \frac 14 x + 260$
(b) Image below
(c) $0.25/mi
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Work Step by Step
(a) If $C(x)$ represents the driving cost and $x$ represents the number of miles driven:
$$C(x) = ax + b$$ $$a = \frac{460 - 380}{800 - 480} = \frac{80}{320} = \frac 1 4$$
Now, substitute some of the values into the equation to find the $b$ value.
$$C(x) = ax + b \longrightarrow 380 = (\frac 1 4)(480) + b$$ $$380 = 120 + b$$ $$b = 380 - 120 = 260$$
$$C(x) = \frac 14 x + 260$$
(b) Plot the following points: $(480,380)$ and $(800,460)$. Then draw the line that passes through both points.
(c)
Rate of change (cost increase) = a = $\frac 14 = 0.25$
Since $C(x)$ is in $\$$ and $x$ in miles:
$\$0.25/mi $
