The basketball gym at Kimi'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. Kimi convinced some local businesses to match a fraction of the families' donations. The businesses contribute $12 when a family donates $15. The businesses contribute $20 when a family donates $25.
In this relationship, x represents the amount of money a family donates (in dollars), and y represents the matching contribution (in dollars) from local businesses.
Graph two points for this relationship and the line passing through them.

Let's break this down step by step to find the points and graph the line based on the relationship between family donations (x) and business contributions (y).

1. The first given relationship is:  
   When the family donates \$15, the businesses contribute \$12.  
   This gives us the point $ (15, 12) $.

2. The second given relationship is:  
   When the family donates \$25, the businesses contribute \$20.  
   This gives us the point $ (25, 20) $.

### To find the equation of the line:
Using the two points $ (15, 12) $ and $ (25, 20) $, we can determine the slope $ m $ of the line:
\[
m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{20 - 12}{25 - 15} = \frac{8}{10} = 0.8
\]
Now that we have the slope, we use the point-slope form of the equation:
\[
y - y_1 = m(x - x_1)
\]
Using the point $ (15, 12) $:
\[
y - 12 = 0.8(x - 15)
\]
Simplifying this:
\[
y - 12 = 0.8x - 12
\]
\[
y = 0.8x
\]
Thus, the equation of the line is $ y = 0.8x $.

### Graphing:
- Plot the points $ (15, 12) $ and $ (25, 20) $.
- Draw the line passing through these points, which corresponds to the equation $ y = 0.8x $.

I can create the graph for you, but would you like to see the graphical representation in an image? Let me know if you want any details or explanations on this. 

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Here are 5 questions related to this:
1. What is the slope of the line, and how does it affect the relationship?
2. How would the equation change if the businesses contributed more per donation?
3. What is the business contribution when a family donates \$50?
4. Can you find a different way to express this relationship in terms of percentages?
5. How does the y-intercept affect the equation in this context?

**Tip:** In any real-world problem involving linear relationships, finding the slope helps describe how the two quantities change in relation to each other.

The basketball gym at Kimi'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. Kimi convinced some local businesses to match a fraction of the families' donations. The businesses contribute $12 when a family donates $15. The businesses contribute $20 when a family donates $25. In this relationship, x represents the amount of money a family donates (in dollars), and y represents the matching contribution (in dollars) from local businesses. Graph two points for this relationship and the line passing through them.

Learn how to graph the relationship between family donations and business contributions. This problem covers linear equations, slope calculation, and graphing two points. It is suitable for students in Grades 7-9 and helps visualize donation matching contributions from businesses.

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