Answer
a) $y=13x+900$. See image for sketch.
b) The slope is 13. It represents the cost per chair.
c) The y-intercept is 900. It represents the basic cost to operate the factory in a day before making any chairs.
Work Step by Step
a) Let $x$ represent the number of chairs manufactured and $y$ represent the total cost. Then, we have two points: $(100, 2200)$ and $(300, 4800)$.
Find the slope.
$m=\frac{y_2-y_1}{x_2-x_1}=\frac{4800-2200}{300-100}=13$
Use point slope form to find the linear equation, and then solve for $y$.
$y-2200=13(x-100)$
$y=13x+900$
b) 13. See (a). Slopes represent the rate of change of a function. In this case, it represents the cost per chair.
c) 900. See (a). Y-intercepts represent the y-value when x=0. In this case, the y-intercept represents the cost when 0 chairs are made.
