figuring out price demand equation
When selling burgers at $2.50$ dollar per unit, average sales are $875$ units per night.
When the price was raised to $3.20$ dollar per unit, average sales dropped to $700$ units per night.
Find the price-demand equation and revenue function.
The answer in the back of the book is $p = 6 - 0.004x$.
I understand how we got $-0.004$ using $\frac{3.20-2.50}{700-850}$.
But can anyone please explain where the $6$ comes from?
$\endgroup$1 Answer
$\begingroup$You're trying to find the equation of the line (in the $xp$-plane) that passes through the points $(875, 2.5)$ and $(700, 3.2)$. You've found the slope to be $m = -0.004$. We can now pick either point (say, the first one) and apply the point-slope formula for a line: $$ p - 2.5 = -0.004(x - 875) \iff p = (-0.004x + 3.5) + 2.5 = -0.004x + 6 $$
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