Gradient of ax+by+c=0?

-\frac{a}{b} (rearrange to y=-\frac abx-\frac cb)

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

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

Steps to find a perpendicular bisector of AB?

Find the midpoint of AB, find the gradient of AB, take the negative reciprocal, then use y-y1=m(x-x1).

In a linear model y=mx+c, what do m and c represent?

m is the rate of change (gradient); c is the starting or fixed value (intercept).

How do you show that a point lies on a line?

Substitute its coordinates into the equation and show that both sides are equal.

Straight linesAQA A-Level Maths: Flashcards

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

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Gradient through $(x_1,y_1)$ and $(x_2,y_2)$ ?: $m=\frac{y_2-y_1}{x_2-x_1}$
Equation of the line with gradient $m$ through $(x_1,y_1)$ ?: $y-y_1=m(x-x_1)$
Gradient of $ax+by+c=0$ ?: $-\frac{a}{b}$ (rearrange to $y=-\frac abx-\frac cb$ )
Condition for two lines to be parallel?: Equal gradients: $m_1=m_2$ .
Condition for two lines to be perpendicular?: $m_1m_2=-1$ , so $m_2=-\frac{1}{m_1}$ .
Gradient of a line perpendicular to one with gradient $\frac23$ ?: $-\frac32$
How do you find where a line crosses the $y$ -axis?: Put $x=0$ in the equation.
How do you find where a line crosses the $x$ -axis?: Put $y=0$ in the equation.
Midpoint of $(x_1,y_1)$ and $(x_2,y_2)$ ?: $\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$
Steps to find a perpendicular bisector of $AB$ ?: Find the midpoint of $AB$ , find the gradient of $AB$ , take the negative reciprocal, then use $y-y_1=m(x-x_1)$ .
In a linear model $y=mx+c$ , what do $m$ and $c$ represent?: $m$ is the rate of change (gradient); $c$ is the starting or fixed value (intercept).
How do you show that a point lies on a line?: Substitute its coordinates into the equation and show that both sides are equal.

Exam questions on Straight lines

The line $l_1$ passes through $A(1,2)$ and $B(5,12)$ .
Find the coordinates of the point where $l_1$ crosses the $y$ -axis.2 marks
The line $m$ has equation $3x+4y-12=0$ .
Find the equation of the line parallel to $m$ that passes through the point $(8,-1)$ . Give your answer in the form $ax+by+c=0$ , where $a$ , $b$ and $c$ are integers.2 marks
The points $A(2,1)$ and $B(6,3)$ are given.
Find an equation of the perpendicular bisector of $AB$ , giving your answer in the form $ax+by+c=0$ where $a$ , $b$ and $c$ are integers.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).