Answer
(a) $C(x) = 13x + 900$
(b) Image below. Slope = 13
(c) $13 per chair
Work Step by Step
(a) If $C(x)$ represents the cost of producing x chairs:
$$C(x) = ax + b$$ $$a = \frac{4800 - 2200}{300 - 100} = \frac{2600}{200} = 13$$
Now, substitute some of the values into the equation to find the $b$ value.
$$C(x) = ax + b \longrightarrow 2200 = (13)(100) + b$$ $$2200 = 1300 + b$$ $$b = 2200 - 1300 = 900$$
$$C(x) = 13 x + 900$$
(b) Plot the following points: $(100,2200)$ and $(300,4800)$. Then draw the line that passes through both points.
Slope = a = 13
(c)
Rate of change (cost increase) = a = $13$
Since $C(x)$ is in $\$$ and $x$ in number of chairs:
$\$13 \space per \space chair $