Ratios · Proportional relationships · 4.4

Proportional tables.

Given a table of a proportional relationship, find k from any pair, then use y = kx to complete the table or predict new values.

01 / THE IDEA

See it work.

Watch the method

Tables of proportions

Find k from one row, then fill the rest.

1 / 1
(4, 12)(4,\, 12)
1

Divide y by x

The constant of proportionality is y ÷ x.

k=124=3k = \frac{12}{4} = 3
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
… =
— / WHY IT WORKS

The idea underneath.

k unlocks the table

Compute k = y/x from a known row, then every other y is k times its x.

Why it works

k = 3 fills 1→3, 2→6, 5→15.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

y is proportional to x. When x = 5, y = 10. Find the constant k.

1

Divide y by x

The constant of proportionality is y ÷ x. k = 10/5 = 2

EX 2medium

y is proportional to x. When x = 2, y = 4. Find the constant k.

1

Divide y by x

The constant of proportionality is y ÷ x. k = 4/2 = 2

EX 3hard

y is proportional to x. When x = 4, y = 32. Find the constant k.

1

Divide y by x

The constant of proportionality is y ÷ x. k = 32/4 = 8

04 / COMMON TRAPS

Where students slip.

Trap

Computing a new k for each row.

Fix

k is the same throughout — find it once.

Trap

Reversing x and y.

Fix

k = y ÷ x.

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

y is proportional to x. When x = 4, y = 24. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
C2

y is proportional to x. When x = 4, y = 16. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
C3

y is proportional to x. When x = 2, y = 10. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
C4

y is proportional to x. When x = 2, y = 14. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
Apply

Apply (4)

A1

y is proportional to x. When x = 5, y = 25. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
A2

y is proportional to x. When x = 5, y = 30. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
A3

y is proportional to x. When x = 4, y = 28. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
A4

y is proportional to x. When x = 5, y = 30. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
Extension

Extension (4)

E1

y is proportional to x. When x = 5, y = 10. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
E2

y is proportional to x. When x = 5, y = 15. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
E3

y is proportional to x. When x = 3, y = 18. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.
E4

y is proportional to x. When x = 4, y = 20. Find the constant k.

Need a hint?
  • Find k from one row.
  • Use y = kx for the others.