Equation of a straight line — A/L Combined Mathematics

What must I remember about Equation of a straight line?

• Gradient (Slope) of a straight line passing through points A(x1, y1) and B(x2, y2): m = (y2 - y1) / (x2 - x1) = tan θ, where θ is the inclination angle with positive x-axis (0° ≤ θ < 180°, θ ≠ 90°).
• Forms of Straight Line equations: Gradient-intercept form: y = mx + c (c = y-intercept); Point-gradient form: y - y1 = m(x - x1); Two-point form: (y - y1)/(y2 - y1) = (x - x1)/(x2 - x1); Intercept form: x/a + y/b = 1 (a = x-intercept, b = y-intercept); General linear form: ax + by + c = 0 (gradient m = -a/b).
• Parallel and Perpendicular lines: Two non-vertical lines with gradients m1 and m2 are Parallel if and only if m1 = m2; they are Perpendicular if and only if m1 * m2 = -1.
• Angle θ between two lines with gradients m1 and m2: tan θ = |(m1 - m2) / (1 + m1 * m2)| where 1 + m1 * m2 ≠ 0; acute angle is taken.
• Parametric form of straight line passing through (x1, y1) at inclination θ: (x - x1) / cos θ = (y - y1) / sin θ = r, where r represents directed distance from (x1, y1) to (x, y).

Test yourself (1 minute)

1. Family of parallel lines

   Any line parallel to ax + by + c = 0 can be expressed as ax + by + k = 0; any line perpendicular to it can be expressed as bx - ay + k = 0.

2. Distance formula between parallel lines

   Perpendicular distance between ax + by + c1 = 0 and ax + by + c2 = 0 is d = |c1 - c2| / √(a² + b²).

3. Collinearity test

   Points A, B, C are collinear if gradient(AB) = gradient(BC), or if area of triangle ABC = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)| = 0.

Practise Equation of a straight line questions today

Source: NIE G.C.E. (A/L) Combined Mathematics Resource Book - Pure Mathematics, Unit 18

What comes next?

Next in the syllabus

Where does Equation of a straight line fit in the syllabus?

Year 1 · Term 3