Does a point lie on the line?
A standard method from Equations of straight lines: the steps and worked examples.
Steps
- Substitute the point's x and y into the equation.
- Work out both sides.
- If they are equal, the point lies on the line; if not, it does not.
Worked examples
Example 1: 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 notFor the whole topic, read Equations of straight lines: key points, common mistakes and how the DSE tests it.