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Chapter 4: Q. 641 (page 571)

Marjorie teaches piano. The equation P=35h-250
P models the relation between her weekly profit, P, in dollars and the number of student lessons, s, that she teaches.

鈸� Find Marjorie鈥檚 profit for a week when she teaches no student lessons.

鈸� Find the profit for a week when she teaches 20student lessons.

鈸� Interpret the slope and P鈥搃ntercept of the equation.

鈸� Graph the equation.

Short Answer

Expert verified

The profit for a week is$-250that is loss of $250and profit when 20student lessons is $450. The slope is localid="1647437544019" 35and intercept is localid="1647437529504" -250. The graph will be

Step by step solution

01

Part(a) Step 1. Given Information 

The given equation is:

P=35h-240

where P=weekly profit

h=Number of lessons

02

Part(a) Step 2. Required Profit

When h=0

The equation becomes,

role="math" localid="1647437488650" P=35(0)-250P=-250

That is a loss ofrole="math" localid="1647437494231" $250

03

Part (b) Required Profit

When

h=20,Theequationbecomes,P=35h-250P=35(20)-250P=700-250P=450

04

Part (c) Step 1. Intercept and Slope 

The given equation is comparable to

y=mx+cwherem=slopec=interceptTherefore,P=35h-250m=35c=-250

05

Part (d) Required graph 

The graph of the given equation will be

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