AI generatedRatio, proportion and rates of changeKey Stage 3

Distinguishing direct proportion from a non-zero-intercept line

Direct proportion has the form and its straight-line graph passes through the origin.

  • Direct proportion has the form and its straight-line graph passes through the origin.
  • A straight line with not equal to zero is not direct proportion.
  • Test : a non-zero -intercept rules out direct proportion. A straight line alone is not enough.

Example 1

Does this equation show directly proportional to ? Explain.

Test whether the straight line passes through the origin.
Yes

Example 2

Does this equation show directly proportional to ? Explain.

Test whether the straight line passes through the origin.
No

Remember
Use the worked steps to check your method, not just the final answer.

Your turn

Question 1

Does this equation show directly proportional to ? Explain.

Check answer
Test whether the straight line passes through the origin.
No

At , , so the line does not pass through the origin.

Question 2

Does this equation show directly proportional to ? Explain.

Check answer
Test whether the straight line passes through the origin.
Yes

It has the form and passes through (0, 0).

Question 3

Does this equation show directly proportional to ? Explain.

Check answer
Test whether the straight line passes through the origin.
No

At , , so the line does not pass through the origin.

Question 4

Does this equation show directly proportional to ? Explain.

Check answer
Test whether the straight line passes through the origin.
No

At , , so the line does not pass through the origin.

Question 5

Does this equation show directly proportional to ? Explain.

Check answer
Test whether the straight line passes through the origin.
Yes

It has the form and passes through (0, 0).

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