Year 9 - Linear equations and graphs - Free practice

Year 9 Linear Equations & Graphs Worksheets

Sketch from gradient/intercept, solve from any form.

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10 questions — 4 Foundation, 4 Standard, 2 Extension — with full worked solutions, calibrated to the Victorian Curriculum.

About this worksheet

Why we built it

Year 9 students should be able to look at any linear equation - in any form - and sketch it. These worksheets practise that across the forms they'll meet (y = mx + c, ax + by = c, x = k, y = k) and tie sketching back to solving.

What's covered

Sub-skills your student will practise

  • Sketching from y = mx + c using gradient and intercept
  • Sketching from two known points
  • Sketching horizontal and vertical lines
  • Solving linear equations algebraically
  • Finding the intersection of two lines

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Frequently asked

Questions parents ask about linear equations and graphs

What forms can a linear equation take?

y = mx + c (gradient-intercept form), ax + by + c = 0 (general form), and special cases like x = k (vertical line) and y = k (horizontal line). Year 9 expects students to sketch any of them.

How do students sketch from gradient-intercept form?

Plot the y-intercept (the 'c' value) on the y-axis. Then use the gradient (rise/run) to find a second point. Draw a straight line through both points.

How do students find the intersection of two lines?

Set the equations equal to each other (or use substitution / elimination), solve for x, then substitute back to find y. The intersection point is (x, y). This is a Year 9 preview of simultaneous equations.

Are vertical and horizontal lines linear equations?

Yes - y = k is a horizontal line at height k, and x = k is a vertical line at position k. Vertical lines have an undefined gradient (rise over zero), which Year 9 introduces formally.

Want a real plan for the term?

Worksheets are great for repetition. A Tuterly tutor can spot the specific moves your student keeps getting wrong and fix them in one or two sessions.

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