How do you find the equation of a line through two points?

Find m=\frac{y2-y1}{x2-x1}, then use y-y1=m(x-x1) with either point.

What do 'integer coefficients' mean for ax+by+c=0?

Multiply to clear fractions so a, b, c are whole numbers.

Midpoint of (x1,y1) and (x2,y2)?

\left(\frac{x1+x2}{2},\frac{y1+y2}{2}\right)

Equation of a vertical line through (4,3)?

x=4 (its gradient is undefined).

Quick check of a line equation?

Substitute both given points; each must satisfy it.

Equation of a straight lineEdexcel International A Level Maths: Flashcards

Card 1 of 130 of 13 known

Question

Gradient of the line through $(x_1,y_1)$ and $(x_2,y_2)$?

Tap or press Space to reveal

Tap card or press Space to flip

See all 13 cards

Gradient of the line through $(x_1,y_1)$ and $(x_2,y_2)$ ?: $m=\frac{y_2-y_1}{x_2-x_1}$
Equation of a line with gradient $m$ and $y$ -intercept $c$ ?: $y=mx+c$
Equation of a line with gradient $m$ through $(x_1,y_1)$ ?: $y-y_1=m(x-x_1)$
How do you find the equation of a line through two points?: Find $m=\frac{y_2-y_1}{x_2-x_1}$ , then use $y-y_1=m(x-x_1)$ with either point.
What do 'integer coefficients' mean for $ax+by+c=0$ ?: Multiply to clear fractions so $a$ , $b$ , $c$ are whole numbers.
Gradient of $ax+by+c=0$ ?: $-\frac{a}{b}$
$y$ -intercept of $ax+by+c=0$ ?: $-\frac{c}{b}$
Where does a line meet the $x$ -axis?: Where $y=0$ .
Where does a line meet the $y$ -axis?: Where $x=0$ .
Midpoint of $(x_1,y_1)$ and $(x_2,y_2)$ ?: $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
Equation of a vertical line through $(4,3)$ ?: $x=4$ (its gradient is undefined).
Equation of a horizontal line through $(4,3)$ ?: $y=3$ (its gradient is $0$ ).
Quick check of a line equation?: Substitute both given points; each must satisfy it.

Exam questions on Equation of a straight line

A line $l$ passes through the points $A(2,5)$ and $B(6,13)$ .
Find the coordinates of the point where $l$ meets the $x$ -axis.2 marks
The line $m$ has equation $3x-4y+8=0$ .
Find the $x$ -coordinate of the point on $m$ where $y=7$ .2 marks
A line $l_1$ passes through the points $P(-3,4)$ and $Q(5,-2)$ .
Find an equation of the line $l_1$ , giving your answer in the form $ax+by+c=0$ , where $a$ , $b$ and $c$ are integers.3 marks

See the full worksheet

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).