Slope and angle of inclination: Class 11 practice
The slope m of a line equals tan θ, where θ is the angle it makes with the positive x-axis. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Coordinates
- tan values
The idea behind slope and angle of inclination
The slope m of a line equals tan θ, where θ is the angle it makes with the positive x-axis. Through two points, m = (y₂ − y₁)/(x₂ − x₁). Three points are collinear when the slopes between pairs are equal.
Step-by-step method
- Compute m from two points.
- θ = tan⁻¹(m) (add 180° if m < 0).
- Compare slopes to test collinearity.
Worked example 1 (Basic)
Find the slope of the line through (-1, 2) and (1, 0).
- m = (0 − 2)/(1 − -1)
- = -1
- Answer: -1
Worked example 2 (Standard)
A line has slope -2. Find the angle it makes with the positive x-axis.
- tan θ = -2
- θ = 116.57°
- Answer: 116.57°
Worked example 3 (Challenge)
Are (1, -5), (5, -13) and (9, -20) collinear?
- Slope AB = -2
- Slope BC = -1.75
- Answer: No
Common mistakes and misconceptions
- Swapping the order in numerator and denominator
- Giving a negative angle
Practice questions
- (Basic) Find the slope of the line through (1, -5) and (2, -6).
- (Basic) Find the slope of the line through (-3, 2) and (-2, 4).
- (Standard) A line has slope -1. Find the angle it makes with the positive x-axis.
- (Standard) A line has slope 2. Find the angle it makes with the positive x-axis.
- (Challenge) Are (3, -1), (7, 7) and (11, 15) collinear?
- (Challenge) Are (0, 5), (3, -1) and (6, -7) collinear?
Answer key with full working
- Q1: m = (-6 − -5)/(2 − 1) → = -1 → Answer: -1
- Q2: m = (4 − 2)/(-2 − -3) → = 2 → Answer: 2
- Q3: tan θ = -1 → θ = 135° → Answer: 135°
- Q4: tan θ = 2 → θ = 63.43° → Answer: 63.43°
- Q5: Slope AB = 2 → Slope BC = 2 → Answer: Yes, collinear
- Q6: Slope AB = -2 → Slope BC = -2 → Answer: Yes, collinear
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 slope and angle of inclination 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.