Question

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

(a) Find Marjorie's profit for a week when she teaches no student lessons.

(b) Find the profit for a week when she teaches 20 student lessons.

(c) Interpret the slope and P-intercept of the equation.

(d) Graph the equation.

Short answer

(a)$-250$$

(b) $450$$

(c) Slope is $35$

P intercept is$-250$

(d) Graph is

Step-by-step solution

Part (a) Step 1 Given information 

Marjorie's profit for a week when she teaches no student lessons

$P=35s-250$

Part (a) Step 2 Solution 

We have

$\begin{array}{rcl}P& =& 35s-250\\ P\left(0\right)& =& 35\times 0-250\\ & =& -250\end{array}$

The profit is$-250\$$

Part (b) Step 1 Given information 

The profit for a week when she teaches $20$student lessons

$P=35s-250$

Part (b) Step 2 Solution 

The profit for a week when she teaches $20$student lessons

localid="1645625009370" $\begin{array}{rcl}P& =& 35s-250\\ P& =& 35\times 20-250\\ & =& 700-250\\ & =& 450\end{array}$

Profit for a week when she teaches $20$ student lessons is$450\$$

Part (c) Step 1 Given information 

Interpret the slope and P-intercept of the equation

$P=35s-250$

Part (c) Step 2 Solution 

We have $P=35s-250$

Equation is of the form $y=mx+c$

Slope is $35$

$P$intercept is$-250$

Part (d) Step 1 Given information 

Graph the equation

$P=35s-250$

Part (d) Step 2 Solution 

Graph is