Straight Lines — Class 11 Mathematics
Core Concepts
The slope of a line through (x₁,y₁) and (x₂,y₂) is m=(y₂−y₁)/(x₂−x₁), when x₂≠x₁. A line with slope m through (x₁,y₁) has y−y₁=m(x−x₁).
Worked Examples
Through (2,3) and (5,9), m=6/3=2. Hence y−3=2(x−2), or y=2x−1.
Parallel non-vertical lines have equal slopes. Perpendicular lines have product of slopes −1.
Explained MCQs
- The slope of a horizontal line is 0.
- The slope of a vertical line is undefined.
- Lines with slopes 2 and −1/2 are perpendicular.
Practice
- Find the equation through (−1,4) with slope 3.
- Find the slope of 3x−2y+7=0.