Answer
(a) $C = 6x+3000$
(b) The slope of the graph is 6
It represents the cost to manufacture each oven.
(c) The y-intercept is 3000.
It represents the fixed costs for the manufacturer.
Work Step by Step
(a) It costs $\$9000$ to produce 1000 ovens.
It costs $\$12,000$ to produce 1500 ovens.
We can find the slope:
$m = \frac{12,000-9000}{1500-1000} = \$6/oven$
We can find the y-intercept:
$y = mx+b$
$9000 = 6(1000)+b$
$b = \$3000$
Let $x$ be the number of ovens that are manufactured.
We can write the cost function:
$C = 6x+3000$
(b) The slope of the graph is 6.
This slope is $\$6/oven$, and it represents the cost to manufacture each oven.
(c) The y-intercept is 3000.
This is $\$3000$ and it represents the fixed costs for the manufacturer. That is, $\$3000$ is the cost the manufacturer has to pay even if they don't manufacture any ovens.
