Question

the basketball gym at aishas school was built in the 1940s and needs a lot of repairs. so, the school is asking families for donations to build a new gym. aisha convinced some local businesses to match a fraction of the families donations. this table shows the relationship between the amount of money a family donates (in dollars), x, and the matching contribution (in dollars) from local businesses, y.

x (dollars donated)	y (dollars matched)
$45	$18
$65	$26
$70	$28

according to the values in the table, do x and y have a proportional relationship?
yes
no
write an equation for the relationship between x and y. simplify any fractions.
y =

Explanation:

Step1: Calculate the ratio for each pair

For the first pair: $\frac{y}{x}=\frac{4}{10}=\frac{2}{5}$
For the second pair: $\frac{y}{x}=\frac{18}{45}=\frac{2}{5}$
For the third pair: $\frac{y}{x}=\frac{26}{65}=\frac{2}{5}$
For the fourth pair: $\frac{y}{x}=\frac{28}{70}=\frac{2}{5}$
Since the ratio $\frac{y}{x}$ is constant ($\frac{2}{5}$) for all pairs, $x$ and $y$ have a proportional relationship.

Step2: Write the equation

The general form of a proportional - relationship is $y = kx$, where $k$ is the constant of proportionality. Since $k=\frac{2}{5}$, the equation is $y=\frac{2}{5}x$.

Answer:

1. yes
2. $y=\frac{2}{5}x$