L 4.9 Proportional Vs. Non-Proportional online exercise for | Live ... - Free Printable

To determine whether each relationship is proportional or non-proportional, we need to check if it fits the form y = kx (where k is a constant) and passes through the origin (0,0). If there’s any added constant (like + b where b ≠ 0), or if the ratio y/x isn’t constant, then it’s non-proportional.

Let’s go one by one:

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A: y = -5/9 x

→ This is in the form y = kx. No extra number added. Even though k is negative, that’s okay — proportional relationships can have negative constants.
✔ Proportional

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B: Tia’s dessert cost her $2.50 plus $0.15 per topping.

→ Let’s write this as an equation:
Cost = 2.50 + 0.15 × (number of toppings)
So, y = 0.15x + 2.50 → has a “+2.50” which means when x=0, y≠0.
✘ Non-proportional

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C: Table with x: 6, 11, 15; y: 2, 12, 20

Check ratios y/x:
- 2 ÷ 6 = 1/3 ≈ 0.333...
- 12 ÷ 11 ≈ 1.09
- 20 ÷ 15 ≈ 1.333...

Ratios are NOT equal → not proportional.
Also, let’s see if it’s linear: from x=6 to 11 (+5), y goes 2 to 12 (+10); from x=11 to 15 (+4), y goes 12 to 20 (+8). Slope is 2 both times? Wait — actually, slope between first two points: (12-2)/(11-6) = 10/5 = 2. Between next: (20-12)/(15-11)=8/4=2. So it’s linear with slope 2. But does it pass through origin?

If y = 2x + b, plug in x=6, y=2:
2 = 2(6) + b → 2 = 12 + b → b = -10
So equation is y = 2x - 10 → doesn’t pass through (0,0).
✘ Non-proportional

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D: Graph showing a line starting at (0,7) going down to about (8,3)

→ The line starts at y=7 when x=0 → so y-intercept is 7, not 0.
Even if it’s straight, if it doesn’t go through (0,0), it’s not proportional.
✘ Non-proportional

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E: y = 12.2x - 7

→ Has “-7”, so when x=0, y=-7 ≠ 0.
✘ Non-proportional

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F: An ostrich is running at a speed of 43 miles per hour.

→ Distance = rate × time → d = 43t
This is y = 43x → no added constant. When time=0, distance=0.
✔ Proportional

*(Note: We assume they mean distance vs. time — which is standard for speed problems like this.)*

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G: Table with x: 3, 5, 7; y: 1.5, 2.5, 3.5

Check ratios:
- 1.5 ÷ 3 = 0.5
- 2.5 ÷ 5 = 0.5
- 3.5 ÷ 7 = 0.5

All ratios equal! Also, check if it passes through origin: if x=0, y should be 0. Since slope is 0.5, and y = 0.5x, yes — when x=0, y=0.
✔ Proportional

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H: Graph starting at (0,0) and going up slowly

→ Starts at origin, and appears to be a straight line → so it’s y = kx form.
✔ Proportional

*(Even without exact numbers, since it starts at (0,0) and is linear, it’s proportional.)*

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I: y = x + 1

→ Has “+1”, so when x=0, y=1 ≠ 0.
✘ Non-proportional

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Now group them:

Proportional: A, F, G, H
Non-Proportional: B, C, D, E, I

Wait — let me double-check C again. Earlier I thought it was non-proportional because of the y-intercept, but let me confirm the table values:

x | y
6 | 2
11| 12
15| 20

We found slope = 2, and using point-slope: y - 2 = 2(x - 6) → y = 2x - 12 + 2 → y = 2x - 10 → yes, intercept -10 → not proportional. Correct.

And G: all ratios 0.5 → proportional.

H: graph starts at (0,0) → proportional.

F: speed → distance = 43*time → proportional.

A: direct variation → proportional.

Others have offsets → non-proportional.

Final grouping:

Proportional: A, F, G, H
Non-Proportional: B, C, D, E, I

But wait — let me count the letters: A through I → 9 items.

Proportional: A, F, G, H → 4
Non-proportional: B, C, D, E, I → 5 → total 9. Good.

One more check on H: the graph shows a line starting at (0,0) and increasing — even if shallow, as long as it’s straight and through origin, it’s proportional. Yes.

And D: starts at (0,7) — definitely not.

Okay, confident now.

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Final Answer:
Proportional: A, F, G, H
Non-Proportional: B, C, D, E, I