Two lines
A standard method from Equations of straight lines: the steps and worked examples.
Steps
- Compare slopes:
- different slopes → exactly one intersection;
- same slope, different intercepts → parallel, no intersection;
- same line → infinitely many.
- To find the intersection, solve the two equations simultaneously.
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.