Graphs · Graphing relationships · 3.3

Proportional graphs.

A proportional relationship y = kx graphs as a straight line through the origin (0, 0). The constant k is the slope — how much y rises per 1 of x. For k = 3, x = 4 → y = 12.

01 / THE IDEA

See it work.

Watch the method

Proportional graphs

y = 3x through the origin; x = 4 → y = 12.

1 / 1
-6-666
1

Through the origin

A proportional graph is y = kx with k = 3. Multiply.

y=3×4=12y = 3 \times 4 = 12
02 / YOUR TURN

Practice until it feels automatic.

Your turn

Work it out.

Type a number, e.g. 5.

streak 0
best 0
-6-666
Your answer:
— / WHY IT WORKS

The idea underneath.

y = kx

Proportional graphs pass through (0, 0) and rise by k for each step in x. (Links to the Ratios subject.)

Why it works

No intercept — it starts at the origin.

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A proportional graph has k = 4. Find y when x = 5.

1

Through the origin

A proportional graph is y = kx with k = 4. Multiply. y = 4 \times 5 = 20

EX 2medium

A proportional graph has k = -2. Find y when x = 1.

1

Through the origin

A proportional graph is y = kx with k = -2. Multiply. y = -2 \times 1 = -2

EX 3hard

A proportional graph has k = 2. Find y when x = 5.

1

Through the origin

A proportional graph is y = kx with k = 2. Multiply. y = 2 \times 5 = 10

04 / COMMON TRAPS

Where students slip.

Trap

Expecting a y-intercept.

Fix

A proportional line goes through the origin (b = 0).

Trap

Confusing k with the y-value.

Fix

k is the slope, not a single y.

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 proportional graph has k = -4. Find y when x = 6.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
C2

A proportional graph has k = 3. Find y when x = 6.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
C3

A proportional graph has k = 3. Find y when x = 6.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
C4

A proportional graph has k = 1. Find y when x = 6.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
Apply

Apply (4)

A1

A proportional graph has k = 4. Find y when x = 2.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
A2

A proportional graph has k = -2. Find y when x = 2.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
A3

A proportional graph has k = 1. Find y when x = 4.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
A4

A proportional graph has k = 4. Find y when x = 5.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
Extension

Extension (4)

E1

A proportional graph has k = -3. Find y when x = 5.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
E2

A proportional graph has k = 3. Find y when x = 6.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
E3

A proportional graph has k = -4. Find y when x = 1.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.
E4

A proportional graph has k = 3. Find y when x = 5.

Need a hint?
  • Use y = kx.
  • The line passes through the origin.