Answer
$q=-50x+800$
$R=-50x^{2}+800x$
Work Step by Step
We are given data points $(x,q)$
$(8,400)$ and $(4, 600).$
The line through these points has an equation
$q-q_{1}=\displaystyle \frac{q_{2}-q_{1}}{x_{2}-x_{1}}(x-x_{1})$
$q=\displaystyle \frac{200}{-4}(x-8)+400$
$q=-50x+400+400$
$q=-50x+800$
$R=xq$
$R=-50x^{2}+800x$
