Graphing Proportional Relationships | Worksheet - Free Printable

Final Answer:
The constant of proportionality is 2.

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Explanation:
Let’s look at the first situation: cookies and sugar.

- For every 24 cookies, you need 2 cups of sugar.
- So, for 1 cookie, how much sugar? → 2 cups ÷ 24 cookies = 1/12 cup per cookie.
But wait — the question asks for the constant of proportionality *in the relationship* “number of cookies = k × cups of sugar”.

That means:
cookies = k × sugar
So solve for *k*:
k = cookies ÷ sugar
Using the given values: 24 cookies ÷ 2 cups = 12.

Hold on — let’s double-check the wording.

The problem says:
> “The number of cookies made is proportional to the cups of sugar used.”
So:
cookies = k × sugar

Given: 24 cookies ↔ 2 cups sugar
→ k = 24 ÷ 2 = 12

But then it says:
> “The baker uses 2 cups of sugar for 24 cookies, so another point is (2, 24).”

In the graph, x-axis = cups of sugar, y-axis = number of cookies.
So point (2, 24) means: x = 2, y = 24 → y = kx → 24 = k·2 → k = 12.

✔ So constant of proportionality = 12.

Wait — the worksheet also says:
> “Pick one of the points (0,0) or (2,24)”
and
> “Number of cookies = ___ × cups of sugar”

So: 24 = ? × 2 → ? = 12.

Now check the second situation (flowers & bouquets):

- 5 bouquets use 10 vases → 10 vases for 5 bouquets
- Relationship: number of vases = k × number of bouquets
So: 10 = k × 5 → k = 2

The question asks:
> “What is the constant of proportionality?”
But there are two parts — Task a and Task b.

Looking at the blanks:

- First blank: “Number of cookies = ___ × cups of sugar” → 12
- Second blank: “Amount of Cheddar Cheese (g) = ___ × Number of Bouquets” — wait, no! That seems mismatched.

Actually, rereading carefully:

In Task a (cookies/sugar):
→ “Number of cookies = ___ × cups of sugar” → answer: 12

In Task b:
“Evlyn works at a flower shop… she made 5 seasonal bouquets. She used a total of 10 vases…”
Then:
> “The number of vases, y, is proportional to the number of bouquets, x.”
So: y = kx → 10 = k·5 → k = 2

But the worksheet has two fill-in blanks at the bottom:

> What is the constant of proportionality? ______
> What is the constant of proportionality? ______

So two answers: 12 and 2

However, the instruction says:
“Provide only the final correct answer.” — singular.

But the problem clearly has two separate proportional relationships.

Looking again at the image description (as interpreted):
The first graph is cookies vs. sugar → constant = 12
The second scenario (bouquets/vases) → constant = 2

Since the student is asked to fill in both blanks, and the final answer expected is likely both values, but format says *only the final correct answer*, and it's one line...

Wait — the very last lines in the image say:
> What is the constant of proportionality? ______
> What is the constant of proportionality? ______

So two answers.

But per instruction: “Provide only the final correct answer.” — and since it's one response, and two questions, safest is to give both, separated clearly.

However, standard practice in such worksheets: first blank = 12, second = 2.

Let me verify units:
- cookies = k × sugar (cups) → 24 = k×2 → k=12 ✔️
- vases = k × bouquets → 10 = k×5 → k=2 ✔️

So final answer should be: 12 and 2

But the format says “only the final correct answer” — possibly they expect the answer for the *graph*, which is the first one.

The title says: “Graphing Proportional Relationships”, and the graph shown is cookies vs. sugar, with points (0,0) and (2,24), and the line passes through them.

The slope of that line = rise/run = 24/2 = 12.

The second part (bouquets) is a separate Try It! section — but the two blank lines at the bottom appear under the whole page, likely for both.

Given ambiguity, and that the *graph* is central, and the first constant is what the graph shows, and the instruction says “the” constant (singular), and the graph is labeled clearly — I think the expected final answer is 12.

But wait — the user uploaded the image, and in standard versions of this worksheet (common 7th grade math sheet), the two blanks are:
1. For cookies: 12
2. For vases/bouquets: 2

And the question literally prints two “What is the constant of proportionality?” lines.

Since the assistant must give *only* the final answer, and there are two, the proper way is:
12 and 2

But format says “[Provide only the final correct answer.]” — no extra text.

I will output:
12 and 2

However, to strictly follow “only the final correct answer” as a single value — but there are two tasks.

Rechecking rules: The user did *not* set ExplainAnswer = true, so we omit explanation, and only give Final Answer.

Given the problem has two proportional relationships and two blanks, the correct final answer is two numbers.

I will write:

Final Answer:
12 and 2