# Straight Lines Notes, Class 11 Mathematics | SwaVid

Straight Lines, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers.

Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines

Source: https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines

# Straight Lines

## Formulas and definitions

## Key ideas

## Common mistakes

## Quick checks

## Keep going

## Questions parents ask

## Class 11 Mathematics on SwaVid

### Slope of a line

### Collinearity and parallel or perpendicular lines

### Point-slope and two-point forms

### Slope-intercept and intercept forms

### Distance of a point from a line

### Next chapter

### Related chapter

### All chapters

SwaVid › CBSE › Class 11 › Mathematics › Straight Lines

Notes written by SwaVid from the NCERT textbook.

Class 11 Mathematics, Chapter 9. Key ideas, formulas and common mistakes.

CBSE does not print marks for a single chapter.

Short answer. This chapter introduces the coordinate geometry of straight lines in a two-dimensional plane. Students learn to find slopes, write various algebraic forms of line equations, and compute distances between points and lines.

Source: NCERT Mathematics (Reprint 2026-27) , Chapter 9, Straight Lines

The slope m of a non-vertical line passing through points (x₁, y₁) and (x₂, y₂) is given by m = (y₂ - y₁) / (x₂ - x₁). It is also given by m = tan θ, where θ is the inclination of the line with the positive x-axis.

Two non-vertical lines with slopes m₁ and m₂ are parallel if and only if m₁ = m₂. They are perpendicular if and only if m₁ m₂ = -1. Three points A, B, and C are collinear if the slope of AB equals the slope of BC.

A line passing through (x₀, y₀) with slope m has the equation y - y₀ = m (x - x₀). A line passing through two distinct points (x₁, y₁) and (x₂, y₂) has the equation y - y₁ = [(y₂ - y₁) / (x₂ - x₁)] (x - x₁).

A line with slope m and y-intercept c is given by y = m x + c. A line making non-zero intercepts a and b on the x-axis and y-axis respectively has the equation (x / a) + (y / b) = 1.

The perpendicular distance d from a given point (x₁, y₁) to the line Ax + By + C = 0 is d = |A x₁ + B y₁ + C| / √(A² + B²). The distance between two parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is |C₁ - C₂| / √(A² + B²).

Try each question first. Then tap it to see the answer.

m = (y₂ - y₁) / (x₂ - x₁)

m = (4 - (-2)) / (-1 - 3)

m = 6 / (-4) = -3 / 2

-3 / 2

Use the point-slope form: y - y₀ = m (x - x₀)

Substitute values: y - 3 = -4 (x - (-2))

y - 3 = -4x - 8

4x + y + 5 = 0

4x + y + 5 = 0

d = |A x₁ + B y₁ + C| / √(A² + B²)

d = |3(2) - 4(3) + 1| / √(3² + (-4)²)

d = |6 - 12 + 1| / √(9 + 16)

d = |-5| / √25 = 5 / 5 = 1

1

Conic Sections .

Introduction to Three Dimensional Geometry .

The 14 chapters of Class 11 Mathematics .

The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment.

No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed.

Conic Sections.

SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works.

- Ch 9 NCERT book
- 80 marks, theory paper
- 3 quick checks
- Inverting the slope formula as difference of x over difference of y . Always place the vertical change in the numerator and horizontal change in the denominator: m = (y₂ - y₁) / (x₂ - x₁).
- Applying perpendicular slope condition m₁ m₂ = -1 to horizontal and vertical lines . A vertical line has an undefined slope, so the product formula does not apply. Identify horizontal lines as y = k and vertical lines as x = h directly.
- Using the parallel lines distance formula before making coefficients of x and y identical . Ensure both lines have the exact same coefficients A and B before computing |C₁ - C₂| / √(A² + B²).

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