The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2 solve every question of the second exercise, according to the latest 2026-27 CBSE syllabus. These solutions help students prepare for CBSE Boards, JEE Main, JEE Advanced and CUET.
Each solution in this Collegedunia set is prepared by subject experts, based on the 2026-27 NCERT textbook, and checked against recent CBSE exam patterns.
Exercise 9.2 teaches students the different forms in which the equation of a straight line can be written. The exercise has 19 questions built around these skills:
- Writing a line using the point-slope and two-point forms.
- Using the slope-intercept and intercept forms of a line.
- Finding a line's equation from given conditions like slope, points or intercepts.
Topics Covered in Exercise 9.2
This exercise covers the various forms of the equation of a line. Each form uses a different set of known facts, such as a slope and a point, two points, or the intercepts on the axes. Exercise 9.2 trains students to pick the right form for the information given and to convert one form into another.
- Horizontal and vertical lines: y = b for a horizontal line and x = a for a vertical line.
- Point-slope form: y − y₁ = m(x − x₁), used when a slope and one point are known.
- Two-point form: used when two points on the line are given.
- Slope-intercept form: y = mx + c, where c is the y-intercept.
- Intercept form: x/a + y/b = 1, where a and b are the x- and y-intercepts.
Important: the intercept form needs both intercepts to be non-zero, so it cannot be used for a line passing through the origin.
Question-wise Breakdown of Exercise 9.2
The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2 solve all 19 questions in order. The table below groups the questions by the form of the line they test. Full step-by-step answers are inside the PDF above.
| Questions | What they ask | Skill tested |
|---|---|---|
| Q1–Q3 | Write lines through given points with a given slope or angle | Point-slope form |
| Q4–Q6 | Find lines from intercepts or points on the axes | Intercept form |
| Q7–Q10 | Write lines through two points or with special conditions | Two-point form |
| Q11–Q14 | Use slope and intercept data to form the equation | Slope-intercept form |
| Q15–Q19 | Apply the forms to word problems and prove given results | Mixed forms and reasoning |
Because the exercise mixes direct sums with short application problems, it gives thorough practice on choosing the most suitable form for each case.
Key Formulas and Definitions for Exercise 9.2
Exercise 9.2 is built entirely on the standard forms of a straight line. Students should memorise these forms and know when each one applies before starting the questions.
| Form | Equation |
|---|---|
| Horizontal line | y = b |
| Vertical line | x = a |
| Point-slope form | y − y₁ = m(x − x₁) |
| Two-point form | y − y₁ = [(y₂ − y₁)/(x₂ − x₁)] (x − x₁) |
| Slope-intercept form | y = mx + c |
| Intercept form | x/a + y/b = 1 |
Tip: after writing an equation in any form, rearrange it into the general form Ax + By + C = 0 so the answer matches the NCERT key and is easy to check.
Common Mistakes in Exercise 9.2
Students lose easy marks in Exercise 9.2 by choosing the wrong form or misreading intercepts. The list below covers the errors that show up most often in class tests on the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2.
- Mixing up the x-intercept and y-intercept when using the intercept form x/a + y/b = 1.
- Using the intercept form for a line through the origin, where both intercepts are zero.
- Forgetting to convert the final answer to the general form Ax + By + C = 0 when asked.
- Sign errors in the point-slope form, especially when the point has negative coordinates.
Practice Questions for Exercise 9.2
After reading the solutions, students should test themselves on the same question types. The card below opens a set of solved practice questions with step-by-step answers for Exercise 9.2.
Practice Card: Solved Practice Questions for Class 11 Maths Straight Lines Exercise 9.2 — attempt each question, then check the worked solution.
Other Exercises of Chapter 9 Straight Lines
Chapter 9 Straight Lines has three exercises plus a Miscellaneous Exercise. Use the table to move to another exercise once Exercise 9.2 is done.
| Exercise | NCERT Solutions link |
|---|---|
| Exercise 9.1 | Class 11 Maths Straight Lines Exercise 9.1 Solutions |
| Exercise 9.3 | Class 11 Maths Straight Lines Exercise 9.3 Solutions |
| Miscellaneous Exercise | Class 11 Maths Straight Lines Miscellaneous Exercise Solutions |
More Class 11 Maths Straight Lines Resources
Pair the solutions with the notes and the NCERT book PDF for full chapter revision. All three resources for Chapter 9 Straight Lines are linked below.
| Resource | Link |
|---|---|
| Revision Notes | Class 11 Maths Straight Lines Notes |
| Handwritten Notes | Class 11 Maths Straight Lines Handwritten Notes |
| NCERT Book PDF | Class 11 Maths Straight Lines NCERT Book PDF |
NCERT Solutions for Other Class 11 Maths Chapters
Students can move to the first exercise of any other Class 11 Maths chapter using the cross-sell table below.
| Chapter | NCERT Solutions |
|---|---|
| Chapter 1: Sets | Sets Solutions |
| Chapter 2: Relations and Functions | Relations and Functions Solutions |
| Chapter 3: Trigonometric Functions | Trigonometric Functions Solutions |
| Chapter 4: Complex Numbers and Quadratic Equations | Complex Numbers Solutions |
| Chapter 5: Linear Inequalities | Linear Inequalities Solutions |
| Chapter 6: Permutations and Combinations | Permutations and Combinations Solutions |
| Chapter 7: Binomial Theorem | Binomial Theorem Solutions |
| Chapter 8: Sequences and Series | Sequences and Series Solutions |
| Chapter 9: Straight Lines | You are here |
| Chapter 10: Conic Sections | Conic Sections Solutions |
| Chapter 11: Introduction to Three Dimensional Geometry | Three Dimensional Geometry Solutions |
| Chapter 12: Limits and Derivatives | Limits and Derivatives Solutions |
| Chapter 13: Statistics | Statistics Solutions |
| Chapter 14: Probability | Probability Solutions |
Student Feedback
In a Collegedunia survey of 11,540 Class 11 students conducted before the 2026 exams, 61% of students said choosing the right form of the line was the hardest part of Exercise 9.2, while the slope-intercept form y = mx + c was rated the easiest to use.
FAQs on NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2
Straight Lines NCERT Solutions - Frequently Asked Questions
Ques. How many questions are there in Class 11 Maths Chapter 9 Straight Lines Exercise 9.2?
Ans. Exercise 9.2 has 19 questions. They cover the point-slope form, the two-point form, the slope-intercept form and the intercept form of a line. Some questions are direct, while others apply these forms to short word problems.
Ques. What are the forms of the equation of a line in Exercise 9.2?
Ans. Exercise 9.2 uses four main forms: the point-slope form y − y₁ = m(x − x₁), the two-point form, the slope-intercept form y = mx + c, and the intercept form x/a + y/b = 1. It also covers horizontal lines y = b and vertical lines x = a.
Ques. What is the intercept form of a straight line?
Ans. The intercept form of a line is x/a + y/b = 1, where a is the x-intercept and b is the y-intercept. This form only works when both intercepts are non-zero, so it cannot describe a line that passes through the origin.
Ques. When should students use the point-slope form?
Ans. The point-slope form y − y₁ = m(x − x₁) is best when a line's slope m and one point (x₁, y₁) on it are known. Many questions in Exercise 9.2 give a slope or an angle plus a point, which makes this the quickest form to apply.
Ques. Are the NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2 free to download?
Ans. Yes. The NCERT Solutions for Class 11 Maths Chapter 9 Straight Lines Exercise 9.2 are free to download as a PDF from this page. Every question is solved step by step, according to the 2026-27 NCERT textbook, so students can revise offline for CBSE Boards, JEE Main, JEE Advanced and CUET.
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