A short orientation first. Year 9 graphing covers gradient and intercept, sketching straight lines, midpoint and distance between points, parallel and perpendicular lines, and a first look at parabolas, circles and exponential curves.

Our tutors wrote and checked these questions against the Victorian Curriculum, which is why the wording and the difficulty match what a Year 9 student meets at school.

The usual linear and non-linear relationships errors at Year 9

If your child gets a question wrong here, it is worth checking whether one of these is behind it. They are the linear and non-linear relationships misconceptions RHZ tutors correct most often with Year 9 students:

None of these is a sign of low ability. Each is a reasonable idea that worked in an earlier year and needs replacing, which is exactly what a good explanation, or a tutor, does.

How to practise linear and non-linear relationships at home

Practice works when it is short, regular and specific. For linear and non-linear relationships, our tutors suggest:

For Years 7 to 10, practise the way a test is sat: mixed questions, time limits, full working. Then mark it honestly and re-do the errors.

About the questions on this page

The 10 questions are drawn from 14 eligible items on linear and non-linear relationships in our Year 9 maths bank, all at the easy and at-level tiers. The selection is fixed for this address so a shared link shows the same quiz; press New set of questions or add ?seed= to the address for a different mix. Options are shuffled, no two questions share a stem, and the answer key is fetched from our server only after you submit, so it is not hidden in the page.

Use this page to answer one question well: is linear and non-linear relationships secure at Year 9 level? For the broader picture across every topic and every difficulty tier, the free Skills Check takes about fifteen minutes and produces a report a tutor walks you through.

Year 9 Linear & non-linear relationships notes: the key ideas

A one-page summary of linear and non-linear relationships at Year 9 level, written by RHZ tutors to the Victorian Curriculum. Read it before the quiz, or print it for revision.

Gradient m = rise ÷ run = (y₂ − y₁)/(x₂ − x₁); the y-intercept c is where the line crosses the y-axis.
Sketch y = mx + c from the intercept and gradient, or find both axis intercepts by setting each variable to zero.
Midpoint averages the x-coordinates and the y-coordinates; distance uses Pythagoras: √((x₂ − x₁)² + (y₂ − y₁)²).
Parallel lines share a gradient; perpendicular gradients multiply to −1, so m = 2 pairs with m = −½.
Non-linear graphs: y = x² is a parabola, x² + y² = r² a circle, y = 2ˣ an exponential curve.
Worked example: line through (1, 3) and (3, 11). m = 8/2 = 4. Then 3 = 4 + c gives c = −1, so y = 4x − 1.
Common mistake: calculating gradient as run over rise; the rise (change in y) always goes on top.
Common mistake: taking the perpendicular gradient as just the negative, −2 instead of −½; flip the fraction and change sign.

How to revise this: sketch every line from its intercept and gradient without a table, then check one point by substitution.

Prints the notes only; the quiz is hidden.

How to read a score out of 10

What to do with the result

1. Want the full picture?

The free Skills Check takes about 15 minutes, covers every Year 9 topic including stretch and challenge questions, and sends a same-day topic-by-topic report. A tutor calls to walk you through it, no obligation.

Start the free Skills Check →

2. Printable practice with answers

Our Year 9 practice papers are full-length, curriculum-aligned and come with worked answers, so a student can practise on paper the way the real test is sat.

Browse practice papers →

3. Tutoring in Melbourne's west or online

Small groups from $25 an hour and 1:1 from $35 an hour at our Truganina centre, or online anywhere in Australia. Same tutors, same Skills Check, same progress notes either way.

See Maths tutoring → All tutoring →

Frequently asked questions

Is this Year 9 linear and non-linear relationships quiz free?

Yes, completely: no sign-up, no email, no payment, and you can take it as many times as you like. It is one of 3,261 free practice questions RHZ Tutoring publishes across Prep to Year 12. Press New set of questions, or add ?seed= to the address, for a different selection from the same topic.

Why only 10 questions on one topic?

Because a single-topic set is the most precise free check available: if the score is low, the gap is in linear and non-linear relationships and nowhere else. There are 14 eligible questions on this topic in our Year 9 Maths bank, so several different sets are available before any repeat.

Where do the linear and non-linear relationships questions come from?

From RHZ Tutoring's own Year 9 Maths question bank, written to the Victorian Curriculum, checked by a tutor and passed through an automated quality gate. The same bank feeds our tutoring sessions and the free Skills Check. The questions on this page sit at the easy and at-level tiers.

What should I do if the score is low?

Read the explanation for each incorrect answer first; most gaps in linear and non-linear relationships are one of the misconceptions listed on this page. Then try a second set a few days later. If it is still low, the free Skills Check will show whether the gap is confined to this topic, and a tutor can build a short catch-up plan.

Is there a mixed Year 9 Maths quiz?

Yes. The Year 9 Maths quiz spreads ten questions across every topic for the year, and the hub lists topic quizzes for every year level from Prep to Year 12.

Free Year 9 Linear & non-linear relationships Quiz — 10 Questions, Instant Results

What Year 9 students need to know about linear and non-linear relationships