Last Updated: June 1, 2026

📋 Table of Contents
What is Straight Lines Revision Notes?
Introduction
1. Slope of a Line
2. Various Forms of the Equation of a Line
3. General Equation of a Line
4. Distance of a Point from a Line
5. Shifting of Origin
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics

📋 Table of Contents

What is Straight Lines Revision Notes?
Introduction
1. Slope of a Line
2. Various Forms of the Equation of a Line
3. General Equation of a Line
4. Distance of a Point from a Line
- Distance Between Parallel Lines:
5. Shifting of Origin
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Straight Lines Class 11 Physics Revision — JEE & NEET 2026 Grandmaster Guide

What is Straight Lines Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Slope (m): (y₂ - y₁) / (x₂ - x₁) or \tan θ.

Parallel Lines: m₁ = m₂.

Perpendicular Lines: m₁m₂ = -1.

Slope-Intercept Form: y = mx + c.

Point-Slope Form: (y - y₁) = m(x - x₁).

Distance of a Point (x₁, y₁) from Ax + By + C = 0: |Ax₁ + By₁ + C| / √(A² + B²). 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

Straight Lines are the simplest geometric paths and the Cartesian plane, representing linear relationships and physics, navigation, n data science. Master the slope formula, various forms of line equations (point-slope, intercept), n the distance from a point to a line to excel and coordinate geometry. This class 11 Math Chapter 10 summary provides all essential concepts for JEE and Board exams. Straight lines are the fundamental paths and Euclidean geometry.

1. Slope of a Line

The slope (also called gradient) of a non-vertical line passing through (x₁, y₁) n (x₂, y₂) is given y: m = (y₂ - y₁) / (x₂ - x₁)

Angle of Inclination (θ): If θ is the angle with the positive x-axis, then m = $\tan$ θ.
Conditions:
- If two lines are parallel, their slopes are equal (m₁ = m₂).
- If two lines are perpendicular, the product of their slopes is -1 (m₁m₂ = -1).

2. Various Forms of the Equation of a Line

Depending on the given information, we use different forms:

Horizontal line: y = b.
Vertical line: x = a.
Point-Slope Form: (y - y₁) = m(x - x₁).
Two-Point Form: (y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁).
Slope-Intercept Form: y = mx + c (where c is the y-intercept).
Intercept Form: x/a + y/b = 1 (where a and b are x and y-intercepts).
$**Normal Form:** x \\\\cos ω + y \\\\sin ω = p (p is the perpendicular distance from the origin).$

3. General Equation of a Line

The general form of a linear equation is Ax + By + C = 0.

Slope (m) = -A/B.
y-intercept = -C/B.
x-intercept = -C/A.

4. Distance of a Point from a Line

The perpendicular distance (d) from a point P(x₁, y₁) to the line Ax + By + C = 0 is: d = |Ax₁ + By₁ + C| / √(A² + B²)

Distance Between Parallel Lines:

The distance between two parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is: d = |C₁ - C₂| / √(A² + B²)

5. Shifting of Origin

If the origin (0, 0) is shifted to a new point (h, k) without changing the direction of axes, then the new coordinates (x', y') are related to the old coordinates (x, y) y: x = x' + h n y = y' + k

Comprehensive Exam Strategy (Q&A)

Q1: Find the equation of the line passing through (2, 3) n parallel to the line 3x - 4y + 5 = 0. Answer:

Slope of given line = -A/B = -3/(-4) = 3/4.
Since lines are parallel, slope of new line = 3/4.
Using Point-Slope Form: y - 3 = (3/4)(x - 2)
4y - 12 = 3x - 6 => 3x - 4y + 6 = 0.

Q2: Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0. Answer:

x₁ = 3, y₁ = -5, A = 3, B = -4, C = -26.
d = |3(3) - 4(-5) - 26| / √(3² + (-4)²)
d = |9 + 20 - 26| / 5 = |3| / 5
d = 0.6 units.

Q3: Find the intercept of the line 2x + 3y = 6 on the coordinate axes. Answer:

Divide y 6: 2x/6 + 3y/6 = 1.
x/3 + y/2 = 1.
Comparing with x/a + y/b = 1: x-intercept = 3, y-intercept = 2.

Related Revision Notes

Chapter 9: Sequences and Series
Chapter 11: Conic Sections
[External Reference: NCERT Class 11 Math Chapter 10 (Authoritative Source)]

Conclusion

Straight lines are the ABCs of coordinate geometry. By mastering the various forms of equations and focusing on the relationship between slopes, you can solve any geometry problem involving linear paths. Always sketch your axes first and remember that perpendicular slopes are negative reciprocals! Keep your distance calculations precise and your intercepts well-defined.

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

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Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

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🪤 The 5 Mistakes That Cost Marks

* The equation $ax + by + c = 0$ represents a line if $a$ and $b$ are not both zero. However, a common mistake is assuming the equation is always a line, forgetting that if $a = b = 0$, it doesn't represent a line.
* When finding the equation of a line given two points, students often forget to check if the line is vertical, in which case the equation would be of the form $x = a$.
* A frequent error occurs when calculating the slope of a line given two points $(x_1, y_1)$ and $(x_2, y_2)$, where students forget that the slope $m$ is given by $(y_2 - y_1) / (x_2 - x_1)$ and not the other way around.
* In the context of the angle between two lines, a common oversight is forgetting that the formula $	a \theta = left| \frac{m_2 - m_1}{1 + m_1m_2}

ight| $applies only when the lines are not perpendicular; for perpendicular lines,$ \theta = 90^circ $. * When applying the formula for the distance of a point$ (x_1, y_1) $from a line$ ax + by + c = 0 $, students often neglect the absolute value sign, leading to incorrect signs for the distance; the correct formula is$ \frac{|ax_1 + by_1 + c|}{sqrt{a^2 + b^2}}$.

🔁 Last 5 Minutes Box

Straight Lines Formulas

Slope (m) of a line = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + c
Point-slope form: y - y1 = m(x - x1)
Two-point form: y - y1 = ((y2 - y1) / (x2 - x1))(x - x1)
Normal form: x*\\cos(α) + y*\\sin(α) = p
Distance of a point (x1, y1) from a line Ax + By + C = 0: |Ax1 + By1 + C| / √(A² + B²)
Equation of a line passing through (x1, y1) and having slope m: y - y1 = m(x - x1)
Equation of a line with slope m and y-intercept c: y = mx + c

Last Updated: June 1, 2026

📋 Table of Contents
What is Straight Lines Revision Notes?
Introduction
1. Slope of a Line
2. Various Forms of the Equation of a Line
3. General Equation of a Line
4. Distance of a Point from a Line
5. Shifting of Origin
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics
📚 Related Topics

📋 Table of Contents

What is Straight Lines Revision Notes?
Introduction
1. Slope of a Line
2. Various Forms of the Equation of a Line
3. General Equation of a Line
4. Distance of a Point from a Line
- Distance Between Parallel Lines:
5. Shifting of Origin
Comprehensive Exam Strategy (Q&A)
Related Revision Notes
Conclusion
📚 Related Topics

Straight Lines Class 11 Physics Revision — JEE & NEET 2026 Grandmaster Guide

What is Straight Lines Revision Notes?

[!TIP] 🚀 2-Minute Quick Recall Summary (Save for Exam Day)

Slope (m): (y₂ - y₁) / (x₂ - x₁) or \tan θ.

Parallel Lines: m₁ = m₂.

Perpendicular Lines: m₁m₂ = -1.

Slope-Intercept Form: y = mx + c.

Point-Slope Form: (y - y₁) = m(x - x₁).

Distance of a Point (x₁, y₁) from Ax + By + C = 0: |Ax₁ + By₁ + C| / √(A² + B²). 📥 Download 1-Page Short Notes PDF (Zero-Friction)

Introduction

1. Slope of a Line

The slope (also called gradient) of a non-vertical line passing through (x₁, y₁) n (x₂, y₂) is given y: m = (y₂ - y₁) / (x₂ - x₁)

Angle of Inclination (θ): If θ is the angle with the positive x-axis, then m = $\tan$ θ.
Conditions:
- If two lines are parallel, their slopes are equal (m₁ = m₂).
- If two lines are perpendicular, the product of their slopes is -1 (m₁m₂ = -1).

2. Various Forms of the Equation of a Line

Depending on the given information, we use different forms:

Horizontal line: y = b.
Vertical line: x = a.
Point-Slope Form: (y - y₁) = m(x - x₁).
Two-Point Form: (y - y₁) / (y₂ - y₁) = (x - x₁) / (x₂ - x₁).
Slope-Intercept Form: y = mx + c (where c is the y-intercept).
Intercept Form: x/a + y/b = 1 (where a and b are x and y-intercepts).
$**Normal Form:** x \\\\cos ω + y \\\\sin ω = p (p is the perpendicular distance from the origin).$

3. General Equation of a Line

The general form of a linear equation is Ax + By + C = 0.

Slope (m) = -A/B.
y-intercept = -C/B.
x-intercept = -C/A.

4. Distance of a Point from a Line

The perpendicular distance (d) from a point P(x₁, y₁) to the line Ax + By + C = 0 is: d = |Ax₁ + By₁ + C| / √(A² + B²)

Distance Between Parallel Lines:

The distance between two parallel lines Ax + By + C₁ = 0 and Ax + By + C₂ = 0 is: d = |C₁ - C₂| / √(A² + B²)

5. Shifting of Origin

Comprehensive Exam Strategy (Q&A)

Q1: Find the equation of the line passing through (2, 3) n parallel to the line 3x - 4y + 5 = 0. Answer:

Slope of given line = -A/B = -3/(-4) = 3/4.
Since lines are parallel, slope of new line = 3/4.
Using Point-Slope Form: y - 3 = (3/4)(x - 2)
4y - 12 = 3x - 6 => 3x - 4y + 6 = 0.

Q2: Find the distance of the point (3, -5) from the line 3x - 4y - 26 = 0. Answer:

x₁ = 3, y₁ = -5, A = 3, B = -4, C = -26.
d = |3(3) - 4(-5) - 26| / √(3² + (-4)²)
d = |9 + 20 - 26| / 5 = |3| / 5
d = 0.6 units.

Q3: Find the intercept of the line 2x + 3y = 6 on the coordinate axes. Answer:

Divide y 6: 2x/6 + 3y/6 = 1.
x/3 + y/2 = 1.
Comparing with x/a + y/b = 1: x-intercept = 3, y-intercept = 2.

Related Revision Notes

Chapter 9: Sequences and Series
Chapter 11: Conic Sections
[External Reference: NCERT Class 11 Math Chapter 10 (Authoritative Source)]

Conclusion

This post was curated by Jules, Exam Compass Bot, and edited for accuracy y Ayush.

📚 Related Topics

Continue your revision with these related guides:

🚀 Ready to Ace Your Exam?

Put your knowledge to the test! Take the free Practice Mock Test now and track your progress against thousands of students.

🎬 Watch video explanations on YouTube →

📚 Related Topics

Continue your revision with these related guides:

🪤 The 5 Mistakes That Cost Marks

* The equation $ax + by + c = 0$ represents a line if $a$ and $b$ are not both zero. However, a common mistake is assuming the equation is always a line, forgetting that if $a = b = 0$, it doesn't represent a line.
* When finding the equation of a line given two points, students often forget to check if the line is vertical, in which case the equation would be of the form $x = a$.
* A frequent error occurs when calculating the slope of a line given two points $(x_1, y_1)$ and $(x_2, y_2)$, where students forget that the slope $m$ is given by $(y_2 - y_1) / (x_2 - x_1)$ and not the other way around.
* In the context of the angle between two lines, a common oversight is forgetting that the formula $	a \theta = left| \frac{m_2 - m_1}{1 + m_1m_2}

🔁 Last 5 Minutes Box

Straight Lines Formulas

Slope (m) of a line = (y2 - y1) / (x2 - x1)
Slope-intercept form: y = mx + c
Point-slope form: y - y1 = m(x - x1)
Two-point form: y - y1 = ((y2 - y1) / (x2 - x1))(x - x1)
Normal form: x*\\cos(α) + y*\\sin(α) = p
Distance of a point (x1, y1) from a line Ax + By + C = 0: |Ax1 + By1 + C| / √(A² + B²)
Equation of a line passing through (x1, y1) and having slope m: y - y1 = m(x - x1)
Equation of a line with slope m and y-intercept c: y = mx + c