Ratios · Proportional relationships · 4.1

Proportional or not?

A relationship is proportional if y is always the same multiple of x — that is, y/x is constant (y = kx). If the ratio changes, it isn’t proportional.

01 / THE IDEA

See it work.

Watch the method

Proportional or not?

If y/x is the same for every pair, it’s proportional.

1 / 1
2,62,6
1

Solve

Work it out.

2,62,6
— / WHY IT WORKS

The idea underneath.

Constant ratio

Check whether y ÷ x gives the same value for every pair. If so, y = kx.

Why it works

(2,6) and (4,12): 6/2 = 12/4 = 3.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A table shows (x, y) = (2, 4) and (4, 8). Is y proportional to x?

1

Answer

Yes

EX 2medium

A table shows (x, y) = (2, 6) and (4, 12). Is y proportional to x?

1

Answer

Yes

EX 3hard

A table shows (x, y) = (2, 6) and (4, 15). Is y proportional to x?

1

Answer

No

04 / COMMON TRAPS

Where students slip.

Trap

Checking only one pair.

Fix

The ratio must be the same for ALL pairs.

Trap

Confusing constant difference with constant ratio.

Fix

Proportional means constant ratio, not difference.

05 / QUIZ

Test yourself.

The Test

12 problems across three tiers. Auto-graded on submit. Hints and a full walkthrough on every question. Your work is saved on this device — sign in to keep it across devices.

0/12Answered
How to answerType just the value. Formatting won't trip you up — we ignore spaces, capital letters, commas, and subscript style, so t₁ = 5, d = 3 and t1=5,d=3 both count. For a list of numbers, separate them with commas (e.g. 3, 10, 17).
Core

Core (4)

C1

A table shows (x, y) = (2, 10) and (4, 21). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
C2

A table shows (x, y) = (2, 8) and (4, 16). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
C3

A table shows (x, y) = (2, 8) and (4, 19). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
C4

A table shows (x, y) = (2, 6) and (4, 12). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
Apply

Apply (4)

A1

A table shows (x, y) = (2, 4) and (4, 8). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
A2

A table shows (x, y) = (2, 6) and (4, 14). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
A3

A table shows (x, y) = (2, 4) and (4, 8). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
A4

A table shows (x, y) = (2, 10) and (4, 20). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
Extension

Extension (4)

E1

A table shows (x, y) = (2, 6) and (4, 15). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
E2

A table shows (x, y) = (2, 10) and (4, 21). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
E3

A table shows (x, y) = (2, 6) and (4, 14). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.
E4

A table shows (x, y) = (2, 4) and (4, 9). Is y proportional to x?

Need a hint?
  • Compute y ÷ x for each pair.
  • Same value → proportional.