Find the equation
A standard method from Equations of straight lines: the steps and worked examples.
Steps
- Get the slope m (given, or from two points: m = (y₂ − y₁)/(x₂ − x₁); parallel → same m; perpendicular → −1/m).
- Get one point (x₁, y₁) on the line.
- Point-slope form: y − y₁ = m(x − x₁).
- Tidy into the form the question wants:
- y = mx + c, or
- general form Ax + By + C = 0, usually with integer coefficients and A > 0.
Worked examples
Example 1: The line L passes through (4, 1) and is perpendicular to 2x + y − 5 = 0. Find L and where the two lines meet.
slope of 2x + y − 5 = 0 is −2, so slope of L = 1/2
y − 1 = ½(x − 4)
2y − 2 = x − 4
L: x − 2y − 2 = 0
solve 2x + y = 5 and x − 2y = 2:
x = 12/5, y = 1/5 intersection (12/5, 1/5)For the whole topic, read Equations of straight lines: key points, common mistakes and how the DSE tests it.