Ratios · Proportional relationships · 4.2

The constant k.

In a proportional relationship y = kx, the constant k is the unit rate — how much y changes per 1 of x. Find it by dividing: k = y ÷ x. For (2, 6), k = 3.

01 / THE IDEA

See it work.

Watch the method

The constant of proportionality

(2, 6) → k = 6 ÷ 2 = 3.

1 / 1
(2, 6)(2,\, 6)
1

Divide y by x

The constant of proportionality is y ÷ x.

k=62=3k = \frac{6}{2} = 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 is the unit rate

The constant of proportionality is y per one x; divide any pair to find it.

Why it works

6 per 2 is 3 per 1.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

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

EX 2medium

y is proportional to x. When x = 3, y = 24. Find the constant k.

1

Divide y by x

The constant of proportionality is y ÷ x. k = 24/3 = 8

EX 3hard

y is proportional to x. When x = 2, y = 12. Find the constant k.

1

Divide y by x

The constant of proportionality is y ÷ x. k = 12/2 = 6

04 / COMMON TRAPS

Where students slip.

Trap

Dividing x by y.

Fix

k = y ÷ x, not x ÷ y.

Trap

Using a non-proportional pair.

Fix

k is only constant if the relation is proportional.

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 = 5, y = 20. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
C2

y is proportional to x. When x = 3, y = 12. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
C3

y is proportional to x. When x = 5, y = 35. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
C4

y is proportional to x. When x = 6, y = 24. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
Apply

Apply (4)

A1

y is proportional to x. When x = 2, y = 12. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
A2

y is proportional to x. When x = 2, y = 6. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
A3

y is proportional to x. When x = 5, y = 35. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.
A4

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

Need a hint?
  • Divide y by x.
  • That value is k.
Extension

Extension (4)

E1

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

Need a hint?
  • Divide y by x.
  • That value is k.
E2

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

Need a hint?
  • Divide y by x.
  • That value is k.
E3

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

Need a hint?
  • Divide y by x.
  • That value is k.
E4

y is proportional to x. When x = 3, y = 24. Find the constant k.

Need a hint?
  • Divide y by x.
  • That value is k.