Cambridge International Mathematics

Straight lines (Chapter 14) 307

In this section we see how to graph straight lines given equations in either gradient-intercept or general form.

GRAPHING FROM THE GRADIENT-INTERCEPT FORM

Lines with equations given in the gradient-intercept form are easily graphed by finding two points on the

graph, one of which is they-intercept.

The other can be found by substitution or using the gradient.

Example 7 Self Tutor

Graph the line with equation y=^13 x+2.

Method 1:

They-intercept is 2.

When x=3, y=1+2=3.

) (0,2)and(3,3)lie on the line.

Method 2:

They-intercept is 2

and the gradient=^13

y-step

x-step

So, we start at(0,2)and move to another

point by moving across 3 , then up 1.

GRAPHING FROM THE GENERAL FORM

Remember that the form ax+by=d is called thegeneral formof a line.

The easiest way to graph lines in general form is to use axes intercepts.

Thex-intercept is found by letting y=0.

They-intercept is found by letting x=0.

Example 8 Self Tutor

Graph the line with equation 2 x¡ 3 y=12 using axes intercepts.

For 2 x¡ 3 y=12:

when x=0, ¡ 3 y=12

) y=¡ 4

when y=0, 2 x=12

) x=6

E GRAPHING LINES FROM EQUATIONS [7.6]

x

y

()0 ¡2,

()3 ¡3,

O x

y

3

2 1

O

x

y

• 4

6

23=12xy-

O

x

y

y-intercept

x-intercept

O

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Y:\HAESE\IGCSE01\IG01_14\307IGCSE01_14.CDR Thursday, 2 October 2008 12:29:11 PM PETER