Question

the equation y=15x can be used to determine the amount of money y pauli's pizzeria makes by selling x pizzas . the graph shows the money leo's pizzeria takes in for different numbers of pizzas sold. which pizzeria makes more money per pizza

Answer 1

Answer:

Pauli's pizzeria make more money per pizza

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

Find out the slope of the graph of Leo's pizzeria

looking at the graph take the point (2,24)

The graph show a proportional relationship (the line passes through the origin)

The slope is m=y/x

we have

For x=2, y=24

substitute

m=24/2=$12 per pizza sold

The linear equation is

y=12x

step 2

Compare the slopes

Pauli's pizzeria

we have

y=15x -----> slope m=$15 per pizza sold

Leo's pizzeria

we have

y=12x -----> slope m=$12 per pizza sold

$15 per pizza sold > $12 per pizza sold

therefore

Pauli's pizzeria make more money per pizza

Answer 2

The Pauli's pizzeria makes more money per pizza

Further explanation

A linear equation is an equation with 2 variables  

General formula  

y-y1 = m (x-x1)  

or  

y = mx + c  

Where  

m = straight-line gradient which is the slope of the line  

x1, y1 = the Cartesian coordinate that is crossed by the line  

c = constant  

The formula for a gradient (m) between 2 points in a line  

$\large{\boxed{\bold{m=\frac{y_2-y_1}{x_2-x_1}}}$

Straight line equation, can be stated in:  

• y = mx  
• ax + by = ab  
• y = a  
• x = a  
• etc.  

The graph of this equation is a line  

To choose which pizzeria makes more money per pizza, then we determine the greatest value of y between the two, pauli's pizzeria and leo's pizzeria

• Pauli's pizzeria equation : y = 15x

Leo's pizzeria equation can be determined from the graph

Let take 2 points to determine the straight line equation :

(2,24) and (4,48)

then :

$\displaystyle m=\frac{48-24}{4-2}\\\\m=\frac{24}{2}\\\\m=12$

Line equation :

$\displaystyle y-y1=m(x-x1)\\\\y-24=12(x-2)\\\\y-24=12x-24\\\\y=12x$

y = 12x

So :

• Leo's pizzeria equation : y = 12x

From the two equations it can be seen that the largest value of y is obtained from the Pauli's pizzeria equation y = 15x

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Keywords : pizzeria, money, equation, line