Chapter 9 — Straight Lines

Chapter 9 of the Class 11 Maths NCERT textbook, "Straight Lines", treats lines as coordinate-geometry figures defined through slope-intercept, point-slope, or intercept forms, enabling analysis of parallelism, perpendicularity, and distance.

• Slope as the identity of a line — The chapter makes slope — the tangent of a line's inclination — the central quantity, using it to capture a line's direction and to test whether two lines are parallel or perpendicular through simple slope conditions.
• Many equations, one line — It presents several equation forms — point-slope, two-point, slope-intercept and intercept — teaching you to choose whichever fits the given information, since the same line can be described in whatever form is most convenient.
• Distances between points and lines — The chapter closes with distance methods: the perpendicular distance from a point to a line and the distance between parallel lines, turning geometric separation into an algebraic calculation.

1. 01Slope m = tan θ measures line inclination; undefined for vertical lines (θ = 90°)
2. 02Slope from two points: m = (y₂ - y₁)/(x₂ - x₁) works for acute and obtuse angles
3. 03Parallel lines have equal slopes; perpendicular lines have slopes satisfying m₁m₂ = -1
4. 04Equation forms: point-slope y - y₀ = m(x - x₀), two-point, slope-intercept y = mx + c, intercept x/a + y/b = 1
5. 05Perpendicular distance from point (x₁,y₁) to line Ax + By + C = 0: d = |Ax₁ + By₁ + C|/√(A² + B²)