Grade 9 Linear Relations Worksheets
Free printable linear relations practice for Grade 9 students. Generate problems, solve them on screen or paper, and download as PDF.
Practice Worksheet
Grade 9 Linear Relations Practice
Solve each problem. Show your work.
- 1.Write the equation of a line with slope 4 and y-intercept 5: _____
- 2.Find the slope through (1, 4) and (3, 6): _____
- 3.Find both intercepts of y = 2x - 6: _____
- 4.Write the equation of a line with slope 5 and y-intercept 3: _____
- 5.Find the slope through (2, 2) and (4, 8): _____
- 6.Find both intercepts of y = 4x - 28: _____
Show answer key
- Question 1: y = 4x + 5
- Question 2: 1
- Question 3: x-intercept (3, 0); y-intercept (0, -6)
- Question 4: y = 5x + 3
- Question 5: 3
- Question 6: x-intercept (7, 0); y-intercept (0, -28)
Free Practice Worksheets
Print, solve on paper, then upload a photo for AI feedback and feedback.
Build confidence with approachable problems
Solve each problem. Take your time.
- 1.Identify the slope (m) and y-intercept (b) of the linear equation: y = 3x + 5
- 2.Write the equation of a line in y = mx + b form where the slope (m) is 2 and the y-intercept (b) is -4.
- 3.Find the slope (m) of a line that passes through the points (0, 3) and (2, 7) using the formula m = (y2 - y1) / (x2 - x1).
- 4.Solve for x in the first-degree equation: 2x + 6 = 14
- 5.Given the equation y = -1/2x + 4, find the value of y when x = 6.
- 6.Solve for x in the first-degree equation: 5x - 3 = 12
A selection of topic skills
Solve each problem. Show your work.
- 1.Find the slope and y-intercept of the line given by the equation y = -3/4x + 5.
- 2.A line passes through the points (2, 4) and (4, 10). Calculate the slope of this line.
- 3.Solve for x in the linear equation: 2(x - 3) + 4 = 12.
- 4.A cell phone plan costs a flat fee of 20 per month plus 0.05 per text message sent. Write an equation in the form y = mx + b where y is the total monthly cost and x is the number of text messages sent.
- 5.A gym membership charges an initial sign-up fee of 50 and a monthly rate of 30. If a person has paid a total of 320, how many months have they been a member? Solve using a linear equation.
- 6.Graph the linear relation y = 2x - 3. Identify the coordinates of the x-intercept and the y-intercept.
Practise specific Linear Relations skills
Skill map
How linear relations skills connect
Shore up what feeds in, work through the core skills in order, then move on to what they unlock. A means the skill has an instant answer checker.
Build up first
Core skills — in order
What Your Child Will Learn
Linear relations are the centrepiece of Grade 9 algebra: students learn to recognize, represent, and manipulate straight-line relationships in tables, graphs, equations, and real-world descriptions. They calculate slope from two points or a graph, interpret it as a rate of change, and move fluently between slope-intercept form (y = mx + b) and standard form.
Students solve linear equations with variables on both sides, including those with fractions and brackets, and use these skills to find where two lines intersect — both graphically and algebraically. Word problems connect the abstract algebra to situations like cell phone plans, distance-time scenarios, and break-even points, requiring students to build an equation from a written description rather than just solve one that's already set up.
Because linear relations reappear in analytic geometry (Grade 10), functions (Grade 11), and beyond, fluency here — especially with slope, intercepts, and solving equations cleanly — pays dividends for years. Students also learn to distinguish linear growth from the non-linear growth they'll meet later in quadratics and exponential functions, which is an important conceptual marker for what's ahead.
Skills Covered
- Calculating slope from a graph, table, or two ordered pairs
- Graphing linear relations using slope-intercept and standard form
- Solving linear equations with variables on both sides
- Finding the point of intersection of two linear relations
- Translating word problems into linear equations
- Interpreting slope and intercepts in real-world contexts
Curriculum Aligned: Part of the de-streamed Grade 9 math course (MTH1W in Ontario), where linear relations form the algebra strand and set up analytic geometry the following year.
Parent Tip: If the algebra notation looks unfamiliar to you, focus on the graph instead — ask your teen to show you where the line crosses the y-axis and how steep it is. Connecting the visual (the graph) to the symbols (the equation) is exactly what they're being tested on, and it's a conversation you can have without doing the algebra yourself.
What your child will practice
- Coding for Linear RelationsUse coding to create graphical representations of linear relations and to solve problems involving linear equations.
- Linear vs Non-Linear RelationsDistinguish between linear and non-linear relations by examining characteristics such as first differences.
- Slope and Y-InterceptIdentify and interpret the slope and y-intercept of a linear relation, and connect them to real-world situations.
- Equation of a LineWrite the equation of a line in the form y = mx + b given its characteristics or graph.
- Solving Linear EquationsSolve first-degree equations with one variable, including equations with variables on both sides.
Want Personalized Linear Relations Practice?
Create a free family account for one personalized worksheet and one homework check, with saved work and progress for every learner. Premium unlocks unlimited AI practice and homework checks.
Create a Free AccountFinished the worksheet? Review it with AI feedback
Snap a photo of your child's completed Grade 9 linear relations work and review AI feedback on the answers and steps it can read.
Check my workFrequently Asked Questions
How often should my child practice linear relations?
Short daily practice sessions of 10-15 minutes are more effective than long weekly sessions. Consistency builds lasting understanding.
How do I know if my child is at the right level for these worksheets?
If your child can complete about 70% of the problems correctly, the level is appropriate. If it's too easy or too hard, try an adjacent grade level.
Can I use these worksheets for homeschool?
Yes. The worksheets align with standard curriculum expectations and can supplement any math program. Generate multiple worksheets to create a full practice set.