A proportional relationship is one in which two quantities vary directly with each other. The variable y varies directly as x if
[tex]y=kx[/tex]
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
[tex]\begin{gathered} 56=k8 \\ \text{ Divide both sides of the equation by 8} \\ \frac{56}{8}=\frac{k8}{8} \\ 7=k \end{gathered}[/tex]
Now, to complete the table you have
*Pizzas: 1
[tex]\begin{gathered} y=7\cdot1 \\ y=7 \end{gathered}[/tex]
So a pizza costs $ 7.
*Cost: $14
[tex]\begin{gathered} 14=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{14}{7}=\frac{7x}{7} \\ 2=x \end{gathered}[/tex]
So two pizzas cost $ 14.
*Cost: $35
[tex]\begin{gathered} 35=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{35}{7}=\frac{7x}{7} \\ 5=x \end{gathered}[/tex]
So five pizzas cost $35.
*Pizzas: 8
[tex]\begin{gathered} y=7\cdot8 \\ y=56 \end{gathered}[/tex]
So eight pizzas cost $56.
*Cost: $70
[tex]\begin{gathered} 70=7x \\ \text{Divide both sides of the equation by 7} \\ \frac{70}{7}=\frac{7x}{7} \\ 10=x \end{gathered}[/tex]
So ten pizzas cost $70.
