Question

3/4Lesson 5: INTRODUCTION TO PROPORTIONAL RELATIONSHIPSStudent Government spent $56 on 8cheese pizzas for their last fundraiser.Complete the table and graph to showthe relationship.7056Pizzas1842Gost ($)143570Cost ($)28I1 2 3 4 5 6 7 8 9 10Pizzas

Answer 1

A proportional relationship is one in which two quantities vary directly with each other. The variable y varies directly as x if

$y=kx$

for some constant k, called the constant of proportionality.

In this case, the variable y is the cost of the pizzas, and variable x is the number of pizzas. The constant of proportionality will be

$\begin{gathered} 56=k8 \\ \text{ Divide both sides of the equation by 8} \\ \frac{56}{8}=\frac{k8}{8} \\ 7=k \end{gathered}$

Now, to complete the table you have

*Pizzas: 1

$\begin{gathered} y=7\cdot1 \\ y=7 \end{gathered}$

So a pizza costs $ 7.

*Cost: $14

$\begin{gathered} 14=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \end{gathered}$

So two pizzas cost $ 14.

*Cost: $35

$\begin{gathered} 35=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{35}{7}=\frac{7x}{7} \\ 5=x \end{gathered}$

So five pizzas cost $35.

*Pizzas: 8

$\begin{gathered} y=7\cdot8 \\ y=56 \end{gathered}$

So eight pizzas cost $56.

*Cost: $70

$\begin{gathered} 70=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{70}{7}=\frac{7x}{7} \\ 10=x \end{gathered}$

So ten pizzas cost $70.