Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 177

Gradient

Thegradientof a line passing through

A(x 1 ,y 1 ) and B(x 2 ,y 2 ) is

y-step

x-step

=

y 2 ¡y 1

x 2 ¡x 1

Gradients of parallel and perpendicular lines

² If two lines areparallel, then their gradients are

equal.

² If two lines areperpendicular, then their gradients

arenegative reciprocals.

If the gradient of one line ism, then the gradient

of the other line is ¡

1

m

Theequation of a lineis an equation which connects thexandyvalues for

every point on the line.

The equation of a straight line can be written in:

² gradient-intercept form y=mx+c,or

² general form Ax+By=D.

A Equations of straight lines

gradientm

gradient-A_m~

A line with equation

has gradient

and -intercept.

ymxc

m

yc

=+

equal

gradients

B,(x y ) 22

A,(x y ) 11

d

x-step

y-step

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_07\177CamAdd_07.cdr Thursday, 3 April 2014 5:47:19 PM BRIAN