How to find where a line meets the axes?

Set x=0 for the y-intercept and y=0 for the x-intercept.

What does the gradient mean in C=1.5d+5?

The cost per mile, \pounds1.50.

How do you show three points form a right angle?

Show two gradients multiply to -1.

Equations of straight linesEdexcel A-Level Maths: Flashcards

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Gradient formula for $(x_1,y_1)$ and $(x_2,y_2)$?

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Gradient formula for $(x_1,y_1)$ and $(x_2,y_2)$ ?: $\frac{y_2-y_1}{x_2-x_1}$
Equation of the line with gradient $m$ through $(x_1,y_1)$ ?: $y-y_1=m(x-x_1)$
Gradient of $ax+by+c=0$ ?: $-\frac ab$
Condition for parallel lines?: $m_1=m_2$
Condition for perpendicular lines?: $m_1m_2=-1$
Perpendicular gradient to $m=\frac34$ ?: $-\frac43$
Line through $(1,4)$ and $(5,12)$ ?: $y=2x+2$
How to find where a line meets the axes?: Set $x=0$ for the $y$ -intercept and $y=0$ for the $x$ -intercept.
Distance between two points?: $\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
What does the gradient mean in $C=1.5d+5$ ?: The cost per mile, $\pounds1.50$ .
What does the intercept mean in $C=1.5d+5$ ?: The fixed fee, $\pounds5$ .
Gradient of the line through $(2,3)$ and $(6,11)$ ?: $2$
How do you show three points form a right angle?: Show two gradients multiply to $-1$ .

Exam questions on Equations of straight lines

The line $l_1$ passes through the points $A(1,4)$ and $B(5,12)$ .
Find an equation of the line through $C(6,0)$ that is perpendicular to $l_1$ , giving your answer in the form $ax+by+c=0$ , where $a$ , $b$ and $c$ are integers.2 marks
The line $l$ has equation $3x-4y+12=0$ .
The line $l$ meets the coordinate axes at the points $X$ and $Y$ . Find the area of triangle $OXY$ , where $O$ is the origin.2 marks
The points $P(-2,1)$ , $Q(4,5)$ and $R(6,2)$ are the vertices of a triangle.
Show that $PQ$ is perpendicular to $QR$ .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).