Everything Maths Grade 10

You are also told that lineABhas a gradient (m) of1,5.

Calculate the missing co-ordinate of pointB.

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1a.2GC7 1b.2GC8 1c.2GC9 2.2GCB 3.2GCC 4a.2GCD

4b.2GCF 5.2GCG 6.2GCH

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Straight lines EMA6C

DEFINITION: Straight line

A straight line is a set of points with a constant gradient between any two of the points.

Consider the diagram below with pointsA(x;y),B(x 2 ;y 2 )andC(x 1 ;y 1 ).

 2  1 1 2

 2

 1

1

2

A(x;y)

B(x 2 ;y 2 )

C(x 1 ;y 1 )

x

y

We havemAB=mBC=mACandm=
y 2 y 1
x 2 x 1

=

y 1 y 2

x 1 x 2

The general formula for finding the equation of a straight line is

yy 1

xx 1

=

y 2 y 1

x 2 x 1

where(x;y)is any point

on the line.

This formula can also be written asyy 1 =m(xx 1 ).

The standard form of the straight line equation isy=mx+cwheremis the gradient andcis they-intercept.

Worked example 5: Finding the equation of a straight line

QUESTION

Find the equation of the straight line throughP(1;5)andQ(5; 4).

298 8.3. Gradient of a line