Worksheet for determining proportionality using tables of X and Y values.

Let’s go through each table one by one to see if the values are proportional.

What does “proportional” mean?
Two quantities are proportional if you can multiply every X value by the same number (called the constant of proportionality) to get the Y value. In other words, Y ÷ X should always give the same result — as long as X is not zero.

We’ll check each table by dividing Y by X for each row and seeing if we get the same number every time.

---

Table 1:
X | Y
-4 | -5 → -5 ÷ -4 = 1.25
-3 | -6 → -6 ÷ -3 = 2 ← different!
Not proportional → no

Wait — let me double-check:
Actually, maybe I made a mistake. Let’s recalculate carefully:

Row 1: Y/X = -5 / -4 = 1.25
Row 2: -6 / -3 = 2 → NOT the same → so not proportional → no

But wait — what if it’s not division? Maybe it’s addition or something else? No — proportionality means multiplication by a constant. So if Y = k * X, then k = Y/X must be constant.

So Table 1: ratios are 1.25, 2, 7/3≈2.33, 8 → all different → no

Actually, hold on — let me do this more systematically.

Better approach: For each table, compute Y/X for each row (if X ≠ 0). If all results are equal → yes. Otherwise → no.

Also, if any X=0, then Y must also be 0 for proportionality (since 0*k=0).

Let’s redo with care.

---

Table 1:
(-4, -5): -5/-4 = 1.25
(-3, -6): -6/-3 = 2 → already different → no

Table 2:
(6, -2): -2/6 = -1/3 ≈ -0.333
(7, -1): -1/7 ≈ -0.142 → different → no

Wait — that doesn’t look right. Let me check again.

Actually, maybe I should think differently. What if the relationship is linear but not proportional? Proportional means it passes through origin — so when X=0, Y=0. But here none have X=0 except possibly later tables.

Alternative method: Check if Y/X is constant.

Table 2:
6 → -2 → ratio = -2/6 = -1/3
7 → -1 → -1/7 → not same → no

But wait — let's try Table 3:

Table 3:
(-70, -10): -10/-70 = 1/7
(-56, -8): -8/-56 = 1/7
(-14, -2): -2/-14 = 1/7
(-7, -1): -1/-7 = 1/7 → ALL SAME! → yes

Okay, so Table 3 is proportional.

Now back to Table 1 — definitely not.

Table 2: let's list:

6 → -2 → ratio = -1/3
7 → -1 → ratio = -1/7 → not same → no

Table 4:
6→3 → 3/6=0.5
7→4 → 4/7≈0.57 → not same → no

Table 5:
1→10 → 10
2→20 → 10
7→70 → 10
10→100 → 10 → ALL 10 → yes

Table 6:
1→2 → 2
4→4 → 1 → different → no

Table 7:
20→-32 → -32/20 = -1.6
15→-24 → -24/15 = -1.6
10→-16 → -16/10 = -1.6
5→-8 → -8/5 = -1.6 → ALL SAME → yes

Table 8:
70→-10 → -10/70 = -1/7
63→-9 → -9/63 = -1/7
35→-5 → -5/35 = -1/7
21→-3 → -3/21 = -1/7 → ALL SAME → yes

Table 9:
2→7 → 7/2=3.5
6→21 → 21/6=3.5
18→63 → 63/18=3.5
20→70 → 70/20=3.5 → ALL SAME → yes

Table 10:
-12→-32 → -32/-12 = 8/3 ≈2.666
-9→-24 → -24/-9 = 8/3
-6→-16 → -16/-6 = 8/3
-3→-8 → -8/-3 = 8/3 → ALL SAME → yes

Table 11:
9→3 → 3/9=1/3
36→6 → 6/36=1/6 → different → no

Wait — 3/9=1/3, 6/36=1/6 — not same → no

Table 12:
2→4 → 4/2=2
3→6 → 6/3=2
4→12 → 12/4=3 → different → no

Wait — 4→12 gives 3, others give 2 → not proportional → no

But let me confirm Table 12:

Row1: 2→4 → ratio=2
Row2: 3→6 → ratio=2
Row3: 4→12 → ratio=3 → not same → no

Now let’s summarize:

1) no
2) no
3) yes
4) no
5) yes
6) no
7) yes
8) yes
9) yes
10) yes
11) no
12) no

Wait — I think I made a mistake in Table 2 earlier. Let me recheck Table 2:

Table 2:
6 → -2 → ratio = -2/6 = -1/3
7 → -1 → -1/7 → not same → still no

But what about Table 11?

Table 11:
9→3 → 3/9=1/3
36→6 → 6/36=1/6 → not same → no

Is there any chance I missed something?

Another way: sometimes people check if the ratio between consecutive rows is same, but no — for proportionality, it’s Y/X constant.

Let me verify Table 10 again:

-12 → -32: (-32)/(-12) = 32/12 = 8/3
-9 → -24: 24/9 = 8/3
-6 → -16: 16/6 = 8/3
-3 → -8: 8/3 → yes

Table 7: all -1.6 → yes

Table 8: all -1/7 → yes

Table 9: all 3.5 → yes

Table 5: all 10 → yes

Table 3: all 1/7 → yes

Others: no

So final answers:

1) no
2) no
3) yes
4) no
5) yes
6) no
7) yes
8) yes
9) yes
10) yes
11) no
12) no

I think that’s correct.

Final Answer:
1. no
2. no
3. yes
4. no
5. yes
6. no
7. yes
8. yes
9. yes
10. yes
11. no
12. no