How do you find the line parallel to a given line through a point?

Use the same gradient in y-y1=m(x-x1) with the given point.

How do you find the line perpendicular to a given line through a point?

Use the negative reciprocal gradient in y-y1=m(x-x1).

First step if a line is given as 3x+4y=18?

Rearrange to y=mx+c to read the gradient: m=-\frac34.

Which pair of perpendicular lines cannot use m1m2=-1?

A vertical line and a horizontal line.

How do you show a triangle has a right angle?

Show two sides have gradients whose product is -1.

How do you find where two lines meet?

Solve their equations simultaneously.

Parallel and perpendicular linesEdexcel International A Level Maths: Flashcards

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Condition for two lines to be parallel?

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Condition for two lines to be parallel?: $m_1=m_2$
Condition for two lines to be perpendicular?: $m_1m_2=-1$
What is the negative reciprocal of $m$ ?: $-\frac1m$
Gradient of a line perpendicular to one with gradient $\frac34$ ?: $-\frac43$
Gradient of a line perpendicular to one with gradient $-5$ ?: $\frac15$
How do you find the line parallel to a given line through a point?: Use the same gradient in $y-y_1=m(x-x_1)$ with the given point.
How do you find the line perpendicular to a given line through a point?: Use the negative reciprocal gradient in $y-y_1=m(x-x_1)$ .
First step if a line is given as $3x+4y=18$ ?: Rearrange to $y=mx+c$ to read the gradient: $m=-\frac34$ .
Gradient of $2x+5y=10$ ?: $-\frac25$
Which pair of perpendicular lines cannot use $m_1m_2=-1$ ?: A vertical line and a horizontal line.
How do you show a triangle has a right angle?: Show two sides have gradients whose product is $-1$ .
How do you find where two lines meet?: Solve their equations simultaneously.

Exam questions on Parallel and perpendicular lines

The line $l_1$ has equation $2x+5y=10$ .
Find an equation of the line parallel to $l_1$ that passes through the point $(5,-1)$ .2 marks
The line $l_2$ passes through the points $A(1,2)$ and $B(5,10)$ .
Find an equation of the line through $A$ that is perpendicular to $l_2$ , giving your answer in the form $ax+by+c=0$ with integer $a$ , $b$ and $c$ .2 marks
The line $l$ has equation $4x+3y=24$ . It passes through the points $A(6,0)$ and $B(0,8)$ .
Find an equation of the line through $A$ that is perpendicular to $l$ , giving your answer in the form $ax+by+c=0$ with integer $a$ , $b$ and $c$ .3 marks

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Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).