Worksheet for students to practice graphing proportional relationships using real-world examples like baking cookies and buying cheese.

You're working on Graphing Proportional Relationships, and you’ve uploaded a worksheet with two problems. Let’s solve both step by step and explain the reasoning.

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## ✔ Problem 1: The Baker’s Cookies

> The head baker at Early Bird Bakery makes cookies every day. For every 24 chocolate chip cookies, the baker makes 8 oatmeal raisin cookies. The number of chocolate chip cookies is proportional to the number of sugar cookies. Let’s graph this proportional relationship!

Step 1: Understand the relationship

We’re told:
- For every 24 chocolate chip cookies, there are 8 oatmeal raisin cookies.
- But the problem says: *“The number of chocolate chip cookies is proportional to the number of sugar cookies.”*

⚠️ Wait — there’s a mismatch here. The sentence says “sugar cookies,” but the context is about chocolate chip and oatmeal raisin cookies. This seems like a typo in the worksheet.

Looking at the rest of the problem:

> “The baker uses 4 cups of sugar for 96 cookies...”

And later:

> “Find the constant of proportionality... pick one of the points other than (0, 0) and divide.”

Also, the axes on the graph are labeled:
- x-axis: Cups of Sugar
- y-axis: Number of Cookies

So it’s clear that the intended proportional relationship is between cups of sugar and number of cookies — not between types of cookies.

✔ So we’ll ignore the confusing first sentence and focus on the correct data:

> “The baker uses 4 cups of sugar for 96 cookies, so the point (4, 96) satisfies this relationship.”

> “If proportional relationships include the point (0, 0), then the line goes through the origin.”

> “The baker uses 2 cups of sugar for 48 cookies, so another point is (2, 48).”

> “The baker would use 6 cups of sugar for 144 cookies, so another point is (6, 144).”

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Step 2: Graph the relationship

Plot these points on the coordinate plane:
- (0, 0)
- (2, 48)
- (4, 96)
- (6, 144)

Connect them with a straight line through the origin — this confirms it’s a proportional relationship.

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Step 3: Find the constant of proportionality

In a proportional relationship, y = kx, where k is the constant of proportionality.

Pick any point (other than (0,0)) and compute k = y/x.

Let’s use (2, 48):
> k = 48 ÷ 2 = 24

Check with (4, 96):
> k = 96 ÷ 4 = 24

Check with (6, 144):
> k = 144 ÷ 6 = 24

✔ Constant of proportionality = 24

This means: For every 1 cup of sugar, the baker can make 24 cookies.

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Step 4: Answer the question

> “You can use the constant of proportionality on the graph as (1, 24).”

Yes! Since k = 24, the point (1, 24) lies on the line — meaning 1 cup of sugar → 24 cookies.

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## ✔ Problem 2: Try It!

> At Giselle’s shop, she sold ordered 5 pounds of chocolate cheese for $10 in all. The cost, y, is proportional to the amount of chocolate cheese, x.

Step 1: Identify the proportional relationship

Given:
- 5 pounds → $10
- So, point: (5, 10)

Since it’s proportional, it goes through (0,0).

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Step 2: Graph it

On the graph provided:
- x-axis: Amount of Chocolate Cheese (pounds)
- y-axis: Cost ($)

Plot:
- (0, 0)
- (5, 10)

Draw a straight line through them.

You can also find other points using the constant of proportionality.

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Step 3: Find the constant of proportionality

k = y/x = 10 ÷ 5 = 2

So, cost = 2 × pounds of cheese

That means: Each pound costs $2.

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Step 4: Answer the question

> “What is the constant of proportionality?”

✔ 2

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## ✔ Problem 3: Evelyn at the Flower Shop

> Evelyn works at a flower shop. This morning, she made 5 seasonal bouquets. Evelyn made a total of 30 roses in the bouquets. The number of roses, y, is proportional to the number of bouquets, x.

Step 1: Identify the relationship

Given:
- 5 bouquets → 30 roses
- Point: (5, 30)

Proportional → line through (0,0)

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Step 2: Graph it

On the graph:
- x-axis: Number of Bouquets
- y-axis: Number of Roses

Plot:
- (0, 0)
- (5, 30)

Draw a straight line.

Other points? Use k = y/x = 30/5 = 6 → so (1, 6), (2, 12), etc.

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Step 3: Constant of proportionality

k = 30 ÷ 5 = 6

Meaning: Each bouquet has 6 roses.

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Step 4: Answer the question

> “What is the constant of proportionality?”

✔ 6

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## 🧠 Summary of Answers:

| Problem | Constant of Proportionality |
|---------|------------------------------|
| Baker’s Cookies (Sugar vs. Cookies) | 24 (cookies per cup of sugar) |
| Chocolate Cheese (Cost vs. Pounds) | 2 (dollars per pound) |
| Flower Bouquets (Roses vs. Bouquets) | 6 (roses per bouquet) |

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## 📌 Key Concept Recap:

- A proportional relationship is a linear relationship that passes through the origin (0,0).
- It can be written as y = kx, where k is the constant of proportionality.
- To find k, use any point (x, y) and compute k = y/x.
- On a graph, k is the slope of the line.

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✔ You’ve now solved all parts of the worksheet correctly! Great job understanding proportional relationships.