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2.Straight Lines – Equation & Forms
Class 11 • Mathematics • NCERT
Straight Lines – Equation & Forms
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This lesson explains the equation of a straight line and its standard forms as per NCERT Class 11. Students learn slope, intercepts, and different ways to represent a straight line clearly and correctly.
Lesson Objectives
- Understand the concept of slope of a line.
- Write equations of straight lines.
- Learn different forms of line equations.
- Solve basic NCERT-style problems.
1. Equation of a Straight Line
An equation that represents a straight line in the coordinate plane is called the equation of a straight line.
Every point (x, y) lying on the line satisfies its equation.
2. Slope (Gradient) of a Line
The slope of a straight line is a measure of its steepness.
Slope (m) = (y₂ − y₁) / (x₂ − x₁)
3. Slope–Intercept Form
The equation of a straight line with slope m and y-intercept c is:
y = mx + c
4. Point–Slope Form
The equation of a line passing through point (x₁, y₁) with slope m is:
y − y₁ = m(x − x₁)
5. Two-Point Form
The equation of a line passing through two points (x₁, y₁) and (x₂, y₂) is:
(y − y₁)/(y₂ − y₁) = (x − x₁)/(x₂ − x₁)
6. Simple NCERT Examples
• Equation with slope 2 and intercept 3: y = 2x + 3
• Line through (1,2) with slope 4: y − 2 = 4(x − 1)
• Line through (1,2) with slope 4: y − 2 = 4(x − 1)
Practice Questions (NCERT)
- Define the slope of a line.
- Write the slope–intercept form of a straight line.
- Find the slope of a line passing through (2,3) and (4,7).
- Write the equation of a line with slope 3 and y-intercept −1.
- Write the point–slope form.
- What is the slope of a horizontal line?
- What is the slope of a vertical line?
- Write the equation of a line passing through (0,5) parallel to x-axis.
- How many points are required to determine a line?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- The measure of steepness of a line.
- y = mx + c
- 2
- y = 3x − 1
- y − y₁ = m(x − x₁)
- 0
- Undefined
- y = 5
- Two
- Yes
© Aviate Learning – Straight Lines (NCERT Class 11)