Two Variables, One Line Class 9 Maths Worksheet with Quiz and Activities
Work with slope, intercepts and pairs of lines, and graph a pair of lines in 2D and 3D. On WitKnowLearn you get the Two Variables, One Line Class 9 online quiz, online activities and interactive games, a line lab, a virtual lab and a worksheet-style practice sheet for NCERT Ganita Manjari Chapter 13.
Two Variables, One Line Class 9 Online Quiz
20 questions: 10 easy, 5 average and 5 thinking. Tap an answer and the next question comes up.
Two Variables, One Line Class 9 Activities
👆 Tap a tab to switch: Learn, Games, Labs, Challenges, Virtual Lab and Practice sheet
Two Variables, One Line: the Story of Lines
A short read for Class 9 before you play. These notes follow Chapter 13 of NCERT Ganita Manjari, Part I.
📈 One equation, one line
Every solution of ax + by + c = 0 is a point on a line.
♿ Slope
Rise divided by run tells how steep a line is.
✖ Two lines
A pair of lines can cross, be parallel or coincide.
🚕 Taxi fares
A fixed charge plus a rate gives a line.
📱 Plans
Where two lines meet, two plans cost the same.
🧮 Solving
Add or subtract equations to find the meeting point.
Two Variables, One Line Class 9 Activities
Follow every step on the Number Train. Earn up to 3 stars in every activity.
This page follows NCERT Class 9 Maths Ganita Manjari, Part I, Chapter 13. Students work with equations, slopes, intercepts and pairs of lines.
The activities are pitched at Class 9 level. Students sort pairs of lines by number of solutions, pop true facts, find slopes and intercepts, and solve case studies on taxi fares and mobile plans. The virtual lab graphs a pair of lines in 2D and 3D. Explore more Class 9 maths worksheets on WitKnowLearn after this chapter.
Formulas and facts to know
| Pair of lines | Slopes | Solutions |
|---|---|---|
| Cross | Different | One |
| Parallel | Equal | None |
| Coincident | Equal and same intercept | Infinitely many |
| 2x + y = 6, 2x - y = 2 | -2 and 2 | One: (2, 2) |
How to use this page
- Flip the six cards and try the Line Lab in the Learn tab.
- Play the five games and the five labs to practise each idea.
- Finish the five challenges to collect up to 15 points.
- Graph a pair of lines in the Virtual Lab and look at it in 2D and 3D.
- Take the 20-question online quiz, with assertion and reason and case study questions, and fill in the practice sheet.
Worked examples
y = 2x - 3, so slope 2 and intercept -3.
Rate 13, fixed 25, so 25 + 325 = 350.
20 = 0.1t, so t = 200 minutes.
This Two Variables, One Line worksheet for Class 9 maths gives you online activities and interactive games that make the chapter clear. Every activity has a goal, a hint and a short fact, so students learn while they enjoy.
Complete Guide: NCERT Class 9 Maths Two Variables, One Line Chapter 13
This guide is for Class 9 students, parents and teachers. It covers Chapter 13 of NCERT Ganita Manjari, Part I, and shows how to use the quiz, labs and games on this page.
Introduction to Two Variables, One Line
The chapter links equations in two variables to straight lines, introduces slope and shows how pairs of lines give solutions.
What is there in this chapter
- Linear equations in two variables.
- Graphs as lines.
- Slope of a line.
- Slope intercept form.
- Pairs of lines and solutions.
- Solving pairs of equations.
- Taxi fares and mobile plans.
Learning objectives
- Find solutions of linear equations.
- Find the slope and intercepts of a line.
- Decide the number of solutions of a pair.
- Solve a pair of equations.
- Reason with assertions and case studies.
Learning outcomes
- The student can find that the slope of a 2.5 m rise over 4 m is 0.625.
- The student can find that the lines 2x + y = 6 and 2x - y = 2 meet at (2, 2).
- The student can find that a taxi fare for 25 km is 350 rupees.
- The student can find that two plans cost the same at 200 minutes.
Two Variables, One Line Class 9 resources on this page
| Resource | What it gives |
|---|---|
| Online quiz | 20 questions: 10 easy, 5 average and 5 thinking, with assertion and reason and case study questions and a full review |
| Flip cards | 6 picture cards with one-line rules |
| Line Lab | A hands-on lab with 3 rounds |
| Games | 5 interactive games |
| Labs | 5 activity labs |
| Virtual Lab | 2 experiments and a 2D and 3D pair of lines grapher with aim, procedure, observations and conclusion |
| Challenges | 5 challenges, 15 points in all |
| Practice sheet | A worksheet-style sheet with 16 questions, name and date lines and a live score |
Key facts
| Idea | Rule |
|---|---|
| Slope | Rise / run |
| y = mx + c | Slope m, intercept c |
| Parallel | No solution |
| Coincident | Infinitely many |
| Intersecting | One solution |
| x-intercept | Put y = 0 |
Types of questions you may see
- Find solutions.
- Find slope and intercepts.
- Count solutions of a pair.
- Solve a pair of equations.
- Assertion and reason questions.
- Case studies on taxi fares and plans.
Solved examples
0.625.
2.
(2, 2).
350.
200 minutes.
50 years.
Common mistakes
| Mistake | Correct idea |
|---|---|
| Thinking one equation has one solution. | It has infinitely many. |
| Mixing up rise and run. | Slope is rise divided by run. |
| Forgetting parallel lines never meet. | So the pair has no solution. |
| Taking the y-intercept as the slope. | In y = mx + c the slope is m. |
| Dividing the equation wrongly. | Divide every term, including the constant. |
Two Variables, One Line in daily life
Taxi fares, mobile plans, ramps and roads all use lines, and slope tells how steep or how fast something changes.
Tips for parents and teachers
- Write the equation as y = mx + c.
- Put y = 0 to find the x-intercept.
- Check a solution in both equations.
- Practise one assertion and one case study each week.
Related Class 9 Maths Worksheets
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- ⭕Circles Class 9 Worksheet with MCQs
- 🧩Herons Formula Class 9 Worksheet
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Two Variables, One Line Class 9 FAQs
What is Chapter 13 of NCERT Class 9 Maths Ganita Manjari?
Chapter 13 is Two Variables, One Line. It covers linear equations in two variables, their graphs, slope, the slope intercept form and solving pairs of linear equations.
What is a linear equation in two variables?
It is an equation that can be written as ax + by + c = 0 where a and b are not both zero. Its graph is a straight line.
How many solutions does a linear equation in two variables have?
It has infinitely many solutions. Each point on the line is a solution.
What is the slope of a line?
The slope is the rise divided by the run, that is the change in y divided by the change in x. A ramp that rises 2.5 m over 4 m has slope 0.625.
What is the slope intercept form?
The form y = mx + c, where m is the slope and c is the y-intercept. For 2y = 4x - 6 we get y = 2x - 3, so the slope is 2 and the y-intercept is -3.
Where does a line cut the x-axis?
Put y = 0. For y = mx + c the line cuts the x-axis at x = -c/m.
How many lines have a given slope and pass through a given point?
Exactly one. The point fixes the position and the slope fixes the tilt.
When does a pair of linear equations have exactly one solution?
When the lines have different slopes, so they cross at one point. For a1x + b1y + c1 = 0 and a2x + b2y + c2 = 0 this means a1/a2 is not equal to b1/b2.
When does a pair have no solution or infinitely many?
No solution when the lines are parallel, with equal slopes and different intercepts. Infinitely many when the lines are the same line, so one equation is a multiple of the other.
How do we solve a pair of equations graphically?
Draw both lines on the same grid and read the point where they cross. For 2x + y = 6 and 2x - y = 2 the lines cross at (2, 2).
How are these ideas used in real life?
A taxi fare of a fixed charge plus a rate per km is a line. Comparing two mobile plans means finding where two lines meet.
What can students do on this page?
Students can take a 20-question online quiz with assertion and reason and case study questions, play five games, try five online activities, finish five challenges, run the Line Lab, do two virtual experiments, graph a pair of lines in 2D and 3D, and fill in a 16-question practice sheet with a Show answers button.
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