Year 9 - Linear equations and graphs - Free practice
Year 9 Linear Equations & Graphs Worksheets
Sketch from gradient/intercept, solve from any form.
Generate a free maths worksheet
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
More Year 9 topics
Other free Year 9 worksheet generators
Year 9
Quadratics
Year 9
Algebra
Year 9
Trigonometry
Year 9
Pythagoras (applied)
Year 9
Surface area and volume
Year 9
Coordinate geometry
Year 9
Exponent laws
Year 9
Scientific notation
Year 9
Simple interest
Year 9
Statistics
Year 9
Probability
Or generate any topic from the full worksheet builder.
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.
Talk to a human
Talk to us about Year 9 linear equations and graphs.
Call or message us with your student's year level and what's tripping them up - we'll point you to the right tutor.