Question

The given graph shows the fee $\left(y\right)$ charged by Academy A based on the number of hours $\left(x\right)$ of swimming lessons.

The following table shows the fee $\left(y\right)$ charged by Academy B based on the number of hours $\left(x\right)$ of swimming lessons.

Fee $\left(\$\right)$	$1.5$	$3$	$4.5$	$6$
Number of hours	$1$	$2$	$3$	$4$

Which academy offers a better deal for swimming lessons?

• A. Academy B
• B. Both academies charge the same fee.
• C. Academy A
• D. The given data is insufficient.

Answer 1

The correct option is C Academy A

Identify the coordinates of any point on the line in the given graph to find the constant of proportionality of the fee changed by Academy A.
Let’s consider the point $(6,8),i.e.,x=6,y=8.$
Ratio of the y-coordinate to the $x-$ coordinate $=\frac{y}{x}=\frac{8}{6}=1.3$
The constant of proportionality for Academy $A$ is $\mathrm{1.3.}$
Constant of proportionality for Academy $B=\frac{1.5}{1}=\frac{3}{2}=\frac{4.5}{3}=\frac{6}{4}=1.5$
$1.3<\mathrm{1.5.}$ Hence, Academy A offers a better deal for swimming lessons.