The basketball gym at Zane's 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. Zane 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)

$20

$11

$40

$22

$60

$33

$100

$55

According to the values in the table, do *x* and *y* have a proportional relationship?

To determine if $ x $ (the amount of money a family donates) and $ y $ (the matching contribution from local businesses) have a proportional relationship, we need to check if the ratio $ \frac{y}{x} $ is constant for all values in the table.

Let's calculate the ratio $ \frac{y}{x} $ for each pair of values:

1. For $ x = 20 $ dollars, $ y = 11 $ dollars:
   \[
   \frac{y}{x} = \frac{11}{20} = 0.55
   \]

2. For $ x = 40 $ dollars, $ y = 22 $ dollars:
   \[
   \frac{y}{x} = \frac{22}{40} = 0.55
   \]

3. For $ x = 60 $ dollars, $ y = 33 $ dollars:
   \[
   \frac{y}{x} = \frac{33}{60} = 0.55
   \]

4. For $ x = 100 $ dollars, $ y = 55 $ dollars:
   \[
   \frac{y}{x} = \frac{55}{100} = 0.55
   \]

Since the ratio $ \frac{y}{x} $ is constant (equal to 0.55) for all values in the table, $ x $ and $ y $ **do** have a proportional relationship.

Would you like more details on how this conclusion was reached, or do you have any other questions?

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Here are 5 related questions to expand on this topic:

1. What does the constant ratio of 0.55 indicate in this context?
2. How would you express the relationship between $ x $ and $ y $ as an equation?
3. If a family donated $150, how much would the businesses contribute based on the proportional relationship?
4. What would the graph of this proportional relationship look like?
5. How does proportionality help in predicting outcomes in real-life situations?

**Tip:** When two quantities have a proportional relationship, their ratio is constant, meaning they increase or decrease at the same rate.

Explore the proportional relationship between the amount families donate and the matching contributions from local businesses at Zane's school gym. Learn how to determine if two quantities have a proportional relationship using real-world data points.

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