Ratios · Proportional relationships · 4.3

Use k to find a value.

Once you know k, the equation y = kx finds any value. If k = 3, then when x = 5, y = 3×5 = 15. This is the power of a proportional relationship.

01 / THE IDEA

See it work.

Watch the method

Use k to find a value

k = 3, x = 5 → y = 15.

1 / 1
y=3x,  x=5y = 3x,\; x = 5
1

Use y = kx

Multiply the constant 3 by x = 5.

y=3×5=15y = 3 \times 5 = 15
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 40.

streak 0
best 0
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— / WHY IT WORKS

The idea underneath.

Predict with y = kx

Multiply the constant by x to get y for any input.

Why it works

k = 3 → y is always 3 times x.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

y = 4x. Find y when x = 9.

1

Use y = kx

Multiply the constant 4 by x = 9. y = 4 × 9 = 36

EX 2medium

y = 5x. Find y when x = 5.

1

Use y = kx

Multiply the constant 5 by x = 5. y = 5 × 5 = 25

EX 3hard

y = 5x. Find y when x = 5.

1

Use y = kx

Multiply the constant 5 by x = 5. y = 5 × 5 = 25

04 / COMMON TRAPS

Where students slip.

Trap

Adding k instead of multiplying.

Fix

y = kx is a multiplication.

Trap

Forgetting which is k.

Fix

k multiplies 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 = 5x. Find y when x = 5.

Need a hint?
  • Multiply k by x.
  • That gives y.
C2

y = 4x. Find y when x = 8.

Need a hint?
  • Multiply k by x.
  • That gives y.
C3

y = 2x. Find y when x = 3.

Need a hint?
  • Multiply k by x.
  • That gives y.
C4

y = 2x. Find y when x = 9.

Need a hint?
  • Multiply k by x.
  • That gives y.
Apply

Apply (4)

A1

y = 2x. Find y when x = 8.

Need a hint?
  • Multiply k by x.
  • That gives y.
A2

y = 5x. Find y when x = 7.

Need a hint?
  • Multiply k by x.
  • That gives y.
A3

y = 6x. Find y when x = 2.

Need a hint?
  • Multiply k by x.
  • That gives y.
A4

y = 8x. Find y when x = 8.

Need a hint?
  • Multiply k by x.
  • That gives y.
Extension

Extension (4)

E1

y = 2x. Find y when x = 3.

Need a hint?
  • Multiply k by x.
  • That gives y.
E2

y = 5x. Find y when x = 5.

Need a hint?
  • Multiply k by x.
  • That gives y.
E3

y = 8x. Find y when x = 4.

Need a hint?
  • Multiply k by x.
  • That gives y.
E4

y = 5x. Find y when x = 9.

Need a hint?
  • Multiply k by x.
  • That gives y.