Question

A hotel manager knows that the number of rooms that guests will rent depends on the price. The hotel's revenue depends on both the price and the number of rooms rented. The table shows the hotel's average nightly revenue based on room price. Use a graph and an equation to find the price that the manager should charge in order to maximize his revenue.

**LINK TO CHART** https://accelerate-educere.brainhoney.com/Resource/27407483,0/Assets/4034_Chart_031913.jpg

Answer 1

Basically, the graph has everything you need to know about the equation! First, find the slope. The left side of the graph is (x), while the right side is (y). Use the slope formula to find the slope.
\[m=\frac{ y_2-y_1 }{ x_2-x_1 }\]
Plug in the numbers for the slope.
\[m=\frac{ 22,400-21,000 }{ 80-70 }\]
\[m=\frac{ 1400 }{ 10 }\]
m = 140

Plug it into the y=mx+b formula.
y = 140x + b

Plug in (x, y) from the graph into the equation.
(21000) = 140(70) + b
21000 = 9800 + b
21000 - 9800 = 9800 - 9800+ b
11200 = b

The equation is y = 140x + 11200

Here's the graph.
http://www.wolframalpha.com/input/?i=y+%3D+140x+%2B+11200

Answer 2

thank you!