Finding the equation of a line: Class 11 practice
A line is fixed by a point and a slope (y − y₁ = m(x − x₁)) or by two points (slope first). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Slope
- Linear equations
The idea behind finding the equation of a line
A line is fixed by a point and a slope (y − y₁ = m(x − x₁)) or by two points (slope first). Parallel lines share a slope; perpendicular slopes multiply to −1.
Step-by-step method
- Find the slope.
- Use point-slope form.
- Rearrange to ax + by + c = 0 and check with a point.
Worked example 1 (Basic)
Find the equation of the line through (-1, 3) with slope 3.
- y − 3 = 3(x − -1)
- y = 3x + 6
- Answer: y = 3x + 6
Worked example 2 (Standard)
Find the equation of the line through (0, 1) and (1, 4).
- m = (4 − 1)/(1 − 0) = 3
- y = 3x + 1
- Answer: y = 3x + 1
Worked example 3 (Challenge)
Find the line through (-3, -2) perpendicular to y = 2x + 1. Write it as x + 2y = c.
- Perpendicular slope = −1/2
- y − -2 = −(1/2)(x − -3) → x + 2y = -7
- Answer: x + 2y = -7
Common mistakes and misconceptions
- Using the same slope for perpendicular lines
- Sign errors when rearranging
Practice questions
- (Basic) Find the equation of the line through (5, -1) with slope -3.
- (Basic) Find the equation of the line through (2, -1) with slope -2.
- (Standard) Find the equation of the line through (1, 1) and (2, 3).
- (Standard) Find the equation of the line through (1, 4) and (3, 10).
- (Challenge) Find the line through (-5, 2) perpendicular to y = 2x + 1. Write it as x + 2y = c.
- (Challenge) Find the line through (-4, 2) perpendicular to y = -4x + 1. Write it as x + -4y = c.
Answer key with full working
- Q1: y − -1 = -3(x − 5) → y = -3x + 14 → Answer: y = -3x + 14
- Q2: y − -1 = -2(x − 2) → y = -2x + 3 → Answer: y = -2x + 3
- Q3: m = (3 − 1)/(2 − 1) = 2 → y = 2x − 1 → Answer: y = 2x − 1
- Q4: m = (10 − 4)/(3 − 1) = 3 → y = 3x + 1 → Answer: y = 3x + 1
- Q5: Perpendicular slope = −1/2 → y − 2 = −(1/2)(x − -5) → x + 2y = -1 → Answer: x + 2y = -1
- Q6: Perpendicular slope = −1/-4 → y − 2 = −(1/-4)(x − -4) → x + -4y = -12 → Answer: x + -4y = -12
Syllabus note
This skill is listed under "Straight Lines" for Class 11 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is finding the equation of a line in?
"Straight Lines", Class 11 Maths (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.