Question

Stella has a home business selling gourmet pizzas. The equation $C=4p+25$models the relation between her weekly cost, C, in dollars and the number of pizzas, p, that she sells.

ⓐ Find Stella’s cost for a week when she sells no pizzas.

ⓑ Find the cost for a week when she sells 15 pizzas.

ⓒ Interpret the slope and C-intercept of the equation.

ⓓ Graph the equation.

Short answer

ⓐ$25

ⓑ$85

ⓒThe slope, 4, means that the weekly cost, C, increases by $4 when the number of pizzas sold, p, increases by 1. The C-intercept means that when the number of pizzas sold is 0, the weekly cost is $25.

ⓓ Graph of the equation

Step-by-step solution

Step 1. Given Information  

Stella has a home business selling gourmet pizzas. The equation $C=4p+25$models the relation between her weekly cost, C, in dollars and the number of pizzas, p, that she sells.

Step 2. Required to find  

ⓐ Find Stella’s cost for a week when she sells no pizzas.

ⓑ Find the cost for a week when she sells 15 pizzas.

ⓒ Interpret the slope and C-intercept of the equation.

ⓓ Graph the equation.

Step 3. Cost for a week when no pizzas were sold 

Put $p=0$in the equation $C=4p+25$

$C=4\left(0\right)+25$

$C=0+25$

$C=25$

Step 4. Cost for a week when 15 pizzas were sold

Put $p=15$in the equation $C=4p+25$

$C=4\left(15\right)+25$

$C=60+25$

$C=85$

Step 5. Interpreting the slope and C-intercept of the equation 

The equation $C=4p+25$is in slope-intercept form $y=mx+b$.

by comparison, we get, slope, $m=4$, which means that the weekly cost, C, increases by $4 when the number of pizzas sold, p, increases by 1. The C-intercept means that when the number of pizzas sold is 0, the weekly cost is $25.

Step 6. Graphing the equation  

Graphing the equation $C=4p+25$

Take two points to graph the line: localid="1645500082869" $(0,25),(10,65)$