Equations of straight lines・Form 4 maths

Read the line Ax + By + C = 0

A standard method from Equations of straight lines: the steps and worked examples.

Steps

Feature	Formula
slope	−A/B
y-intercept	−C/B (put x = 0)
x-intercept	−C/A (put y = 0)

Safer: put x = 0 and y = 0 yourself rather than memorising.

Worked examples

Example 1: The line through (2, −1) with slope 3.

y − (−1) = 3(x − 2)
y + 1 = 3x − 6
y = 3x − 7

Example 2: The line through A(−1, 4) and B(3, −4).

m = (−4 − 4)/(3 − (−1)) = −8/4 = −2
y − 4 = −2(x + 1)
y = −2x + 2

Example 3: 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)

Example 4: Does a point lie on the line 3x − 4y + 6 = 0: test (2, 3) and (1, 2).

(2, 3):  3(2) − 4(3) + 6 = 6 − 12 + 6 = 0     ✓ lies on the line
(1, 2):  3(1) − 4(2) + 6 = 3 − 8 + 6 = 1 ≠ 0  ✗ does not

For the whole topic, read Equations of straight lines: key points, common mistakes and how the DSE tests it.

Steps

Worked examples

Other methods in this topic