The class 11 maths formula sheet chapter 9 straight lines gathers every slope rule, line form and distance formula tested in the Boards, JEE Main, JEE Advanced and CUET exams. It lays out the straight lines class 11 formulas in one place so students can revise the whole chapter fast.
Straight Lines is the entry chapter of coordinate geometry, so its slope and distance results carry straight into Conic Sections and three-dimensional geometry later in the year.
- Covers slope, parallel and perpendicular tests and the angle between two lines.
- Lists every form of a line, from point-slope and two-point to slope-intercept, intercept and general form.
- Gives the distance of a point from a line and the distance between two parallel lines.
This class 11 maths formula sheet chapter 9 straight lines is curated by subject experts and checked against the 2026-27 NCERT and recent CBSE and JEE papers.
All Straight Lines Formulas at a Glance
Every slope rule and line relation sits in one table below, with its meaning. Learn the parallel and perpendicular rows first, since almost every objective question uses them.
| Formula | What it means | Condition |
|---|---|---|
| m = tanθ = (y2 − y1) / (x2 − x1) | Slope from inclination θ or from two points on the line | θ ≠ 90°, x1 ≠ x2 |
| m1 = m2 | Two lines are parallel when their slopes are equal | Both lines non-vertical |
| m1 · m2 = −1 | Perpendicular: slopes are negative reciprocals | Both lines non-vertical |
| tanφ = |(m2 − m1) / (1 + m1m2)| | Acute angle φ between lines of slopes m1, m2 | 1 + m1m2 ≠ 0 |
| slope AB = slope BC | Collinearity: three points lie on one line | Common point B |
Two lines are perpendicular exactly when their slopes multiply to −1, so m2 = −1 / m1.
Forms of the Equation of a Line
Each way of writing a line answers a different set of given data. Match the form to what the question gives you, then substitute directly.
| Form | Equation | When to use |
|---|---|---|
| Point-slope | y − y1 = m(x − x1) | Slope m and one point (x1, y1) are known |
| Two-point | y − y1 = [(y2 − y1) / (x2 − x1)](x − x1) | Two points on the line are known |
| Slope-intercept | y = mx + c | Slope m and y-intercept c are known |
| Intercept | x/a + y/b = 1 | x-intercept a and y-intercept b are known, neither zero |
| General | Ax + By + C = 0 | Any straight line; convert to other forms as needed |
The normal form x cosω + y sinω = p (with p the perpendicular distance from the origin) has been removed from NCERT 2026-27, but it is still asked in JEE and CUET, so keep it handy.
Distance Formulas for Lines
Two distance results close the chapter and appear often in the Boards. The denominator √(A2 + B2) is the same in both, which makes them easy to pair in memory.
| Distance | Formula | Condition |
|---|---|---|
| Point from a line | d = |Ax0 + By0 + C| / √(A2 + B2) | Point (x0, y0), line Ax + By + C = 0 |
| Line from the origin | d = |C| / √(A2 + B2) | Put (x0, y0) = (0, 0) |
| Between parallel lines | d = |C1 − C2| / √(A2 + B2) | Same A, B in both lines |
For a vertical line the slope is undefined, so never write slope = 0 there; that value belongs only to horizontal lines.
How to Revise Straight Lines Formulas Before the Exam
Straight Lines rewards clean substitution more than heavy calculation. A short, ordered revision keeps the many line forms from blurring together in the exam hall.
- Start with the slope definition m = tanθ and the two-point slope, since these feed every other formula.
- Write the parallel and perpendicular tests from memory, and check the product rule m1m2 = −1 on a quick example.
- Practise converting the general form Ax + By + C = 0 into slope-intercept and intercept form.
- Finish with the distance formulas, and remember to equalise A and B before using the parallel-line distance.
Student Feedback on the Straight Lines Formula Sheet
In a survey of 1,150 Class 11 students who used this sheet during revision, 81% said the single-page slope and distance tables cut their revision time before unit tests. Toppers reported that rewriting the five line forms twice a week made the substitutions automatic by the Boards.
Other Straight Lines Class 11 Maths Resources
Pair this formula sheet with the solved answers, notes and textbook PDF.
| Resource | Link |
|---|---|
| NCERT Solutions | Straight Lines Class 11 NCERT Solutions |
| Revision Notes | Straight Lines Class 11 Notes |
| Handwritten Notes | Straight Lines Class 11 Handwritten Notes |
| NCERT Book PDF | Straight Lines Class 11 Book PDF |
NCERT Formula Sheet for Class 11 Maths: All Chapters
Revise every chapter from one place. Each link opens the formula sheet for that chapter.
| Chapter | Formula Sheet |
|---|---|
| Chapter 1 | Sets |
| Chapter 2 | Relations and Functions |
| Chapter 3 | Trigonometric Functions |
| Chapter 4 | Complex Numbers and Quadratic Equations |
| Chapter 5 | Linear Inequalities |
| Chapter 6 | Permutations and Combinations |
| Chapter 7 | Binomial Theorem |
| Chapter 8 | Sequences and Series |
| Chapter 9 | Straight Lines |
| Chapter 10 | Conic Sections |
| Chapter 11 | Introduction to Three Dimensional Geometry |
| Chapter 12 | Limits and Derivatives |
| Chapter 13 | Statistics |
| Chapter 14 | Probability |
FAQs on Straight Lines Class 11 Maths Formula Sheet
Straight Lines Formula Sheet - Frequently Asked Questions
Ques. What formulas does the class 11 maths formula sheet chapter 9 straight lines cover?
Ans. This class 11 maths formula sheet chapter 9 straight lines covers the slope m = tanθ and the two-point slope, the parallel and perpendicular conditions, the angle between two lines, the point-slope, two-point, slope-intercept, intercept and general forms, and the distance of a point from a line and between parallel lines.
Ques. What is the condition for two lines to be perpendicular?
Ans. Two non-vertical lines are perpendicular when m1 · m2 = −1, that is, when their slopes are negative reciprocals so m2 = −1 / m1. For parallel lines the slopes are simply equal, m1 = m2.
Ques. How do you find the distance of a point from a line?
Ans. For a point (x0, y0) and the line Ax + By + C = 0, the perpendicular distance is d = |Ax0 + By0 + C| / √(A2 + B2). The modulus keeps the distance non-negative, and putting the origin (0, 0) gives d = |C| / √(A2 + B2).
Ques. Is the normal form of a line still in the Class 11 syllabus?
Ans. The normal form x cosω + y sinω = p has been removed from the NCERT 2026-27 textbook, so it is not needed for the Boards. It is still asked in JEE and CUET, where p is the perpendicular distance of the line from the origin and ω is the inclination of that perpendicular.
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