Year 10 Straight Line Graphs

Parallel and perpendicular line equations

This mini-lesson teaches the exact exam move: find the equation of a line that is parallel or perpendicular to a given line and passes through a given point.

The whole question in one sentence

They give you a line and a point. Your job is to build a new line through that point.

Parallel
same m

The gradient stays exactly the same.

Perpendicular
m1 x m2 = -1

Flip the fraction and change the sign.

The point is not usually on the original line. It belongs to the new line you are building.
Practice structure: 10 original parallel-line questions, then 10 original perpendicular-line questions. Same test shape, fresh numbers.
Teaching sequence

Method

1
Read the original gradient.In y = mx + c, m is the gradient.
2
Choose the new gradient.Parallel: keep m. Perpendicular: use the negative reciprocal.
3
Start the new line.Write y = mx + c using the new gradient.
4
Substitute the point.Put the given x and y into the new line to find c.
5
Write the final equation.The final answer should be y = mx + c.
Exam explanation: Parallel lines have equal gradients. Perpendicular lines have gradients that multiply to -1.

Worked example

Find the equation of the line that is perpendicular to y = (1/2)x + 3 and passes through (4, -1).

Original gradient: 1/2

Perpendicular gradient: -2

Start the new line: y = -2x + c

Substitute (4, -1): -1 = -2(4) + c

Solve: -1 = -8 + c, so c = 7

Final equation: y = -2x + 7

Practice
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