Worksheet on proportional and non-proportional relationships with tables, graphs, and word problems.

Let’s solve each problem step by step. We’ll check if the relationship is proportional — that means, does it start at (0,0) and go up in a straight line with the same rate? Or, for tables: do all the ratios of y/x stay the same?

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Problem 1: Popcorn Machine Rental

Cost = $20 per hour + $32 fee

So:
- 1 hour → 20×1 + 32 = $52
- 2 hours → 20×2 + 32 = $72
- 3 hours → 20×3 + 32 = $92
- 4 hours → 20×4 + 32 = $112

Table:

| Hours | Cost ($) |
|-------|----------|
| 1 | 52 |
| 2 | 72 |
| 3 | 92 |
| 4 | 112 |

Check ratios (Cost ÷ Hours):
- 52 ÷ 1 = 52
- 72 ÷ 2 = 36 ← different!
→ Not proportional because the ratio changes. Also, when hours = 0, cost = $32 (not 0), so it doesn’t pass through origin.

✔ Not proportional

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Problem 2: Cakes and Sugar

She needs 2 cups sugar per cake.

So:
- 1 cake → 2 cups
- 2 cakes → 4 cups
- 3 cakes → 6 cups
- 4 cakes → 8 cups

Table:

| Cakes | Sugar (cups) |
|-------|--------------|
| 1 | 2 |
| 2 | 4 |
| 3 | 6 |
| 4 | 8 |

Ratios (Sugar ÷ Cakes):
- 2÷1 = 2
- 4÷2 = 2
- 6÷3 = 2
- 8÷4 = 2 → All same!

Also, if she makes 0 cakes, she uses 0 sugar → passes through (0,0).

✔ Proportional

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Problem 3: CDs at Music Store

Each CD costs $11.99 including tax.

So:
- 1 CD → $11.99
- 2 CDs → 2 × 11.99 = $23.98
- 3 CDs → 3 × 11.99 = $35.97
- 4 CDs → 4 × 11.99 = $47.96

Table:

| CDs | Cost ($) |
|-----|------------|
| 1 | 11.99 |
| 2 | 23.98 |
| 3 | 35.97 |
| 4 | 47.96 |

Ratios (Cost ÷ CDs):
- 11.99 ÷ 1 = 11.99
- 23.98 ÷ 2 = 11.99
- 35.97 ÷ 3 = 11.99
- 47.96 ÷ 4 = 11.99 → All same!

And 0 CDs = $0 → passes through origin.

✔ Proportional

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Problem 4: Jean’s Savings Account

Starts with $280. Adds $30 every week.

So:
- Week 1 → 280 + 30 = $310
- Week 2 → 310 + 30 = $340
- Week 3 → 340 + 30 = $370
- Week 4 → 370 + 30 = $400

Table:

| Weeks | Savings ($) |
|-------|-------------|
| 1 | 310 |
| 2 | 340 |
| 3 | 370 |
| 4 | 400 |

Ratios (Savings ÷ Weeks):
- 310 ÷ 1 = 310
- 340 ÷ 2 = 170 ← different!
→ Not proportional.

Also, at week 0, she already has $280 → not (0,0).

✔ Not proportional

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Problem 5: Temperature (Celsius to Fahrenheit)

Given table:

| Celsius | Fahrenheit |
|---------|------------|
| 0 | 32 |
| 5 | 41 |
| 10 | 50 |
| 15 | 59 |
| 20 | 68 |

We can graph this or check ratios.

But note: At 0°C, it’s 32°F → not (0,0). So already not proportional.

Check ratios anyway:
- 32 ÷ 0 → undefined (but we know it’s not zero)
- 41 ÷ 5 = 8.2
- 50 ÷ 10 = 5 → different from 8.2 → not constant.

Also, formula is F = (9/5)C + 32 → has a “+32”, so not proportional.

✔ Not proportional

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Problem 6: Popcorn Bags and Cost

Table:

| Bags | Cost ($) |
|------|----------|
| 0 | 0 |
| 1 | 4 |
| 2 | 8 |
| 3 | 12 |
| 4 | 16 |

Ratios (Cost ÷ Bags):
- 0÷0 → skip (but point is (0,0))
- 4÷1 = 4
- 8÷2 = 4
- 12÷3 = 4
- 16÷4 = 4 → all same!

Graph would be straight line through origin.

✔ Proportional

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Problem 7: Online DVD Rentals

$15 per month for unlimited rentals.

So:
- Month 1 → $15
- Month 2 → $30
- Month 3 → $45
- Month 4 → $60
etc.

Table (for graphing):

| Month | Cost ($) |
|-------|----------|
| 0 | 0 ← if you rent 0 months, pay $0
| 1 | 15 |
| 2 | 30 |
| 3 | 45 |
| 4 | 60 |

Ratios (Cost ÷ Month):
- 15÷1 = 15
- 30÷2 = 15
- 45÷3 = 15
- 60÷4 = 15 → all same!

And at 0 months, cost = $0 → passes through origin.

✔ Proportional

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Final Answer:

1. Not proportional
2. Proportional
3. Proportional
4. Not proportional
5. Not proportional
6. Proportional
7. Proportional