Graphs · Graphing relationships · 3.4

Proportional or not?

A straight-line graph is proportional only if it passes through the origin (0, 0). A line that crosses the y-axis somewhere else is linear but NOT proportional.

01 / THE IDEA

See it work.

Watch the method

Proportional or not?

Through the origin → proportional; otherwise not.

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-6-666
1

Work it out

— / WHY IT WORKS

The idea underneath.

Check the origin

Proportional graphs are straight AND pass through (0, 0). A non-zero y-intercept breaks proportionality.

Why it works

Does it hit (0, 0)?

03 / WORKED EXAMPLES

From easy to tricky.

EX 1easy

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

1

Answer

No

EX 2medium

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

1

Answer

No

EX 3hard

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

1

Answer

No

04 / COMMON TRAPS

Where students slip.

Trap

Calling every line proportional.

Fix

Only lines through the origin are proportional.

Trap

Ignoring the y-intercept.

Fix

A non-zero intercept means not 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
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Core

Core (4)

C1

A line is straight. Does it represent a proportional relationship (y = kx)? (It passes through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
C2

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
C3

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
C4

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
Apply

Apply (4)

A1

A line is straight. Does it represent a proportional relationship (y = kx)? (It passes through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
A2

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
A3

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
A4

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
Extension

Extension (4)

E1

A line is straight. Does it represent a proportional relationship (y = kx)? (It passes through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
E2

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
E3

A line is straight. Does it represent a proportional relationship (y = kx)? (It does NOT pass through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.
E4

A line is straight. Does it represent a proportional relationship (y = kx)? (It passes through the origin.)

Need a hint?
  • Check whether it passes through (0, 0).
  • A non-zero intercept → not proportional.