Cambridge International Mathematics

Straight lines (Chapter 14) 299

3 Find the equation of:

a thex-axis b they-axis

c a line parallel to thex-axis and three units below it

d a line parallel to they-axis and 4 units to the right of it.

4 Find the equation of:

a the line with zero gradient that passes through(¡ 1 ,3)

b the line with undefined gradient that passes through(4,¡2).

In this section we will graph some straight lines from tables of values. Our aim is to identify some features

of the graphs and determine which part of the equation of the line controls them.

GRAPHING FROM A TABLE OF VALUES

Consider the equation y=2x+1. We can choose any value we like forxand use our equation to find

the corresponding value fory.

We can hence construct atable of valuesfor points on the line.

x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y ¡ 5 ¡ 3 ¡ 1 1 3 5 7

For example: y=2£¡3+1

=¡6+1

=¡ 5

y=2£2+1

=4+1

=5

From this table we plot the points (¡ 3 ,¡5),(¡ 2 ,¡3),

(¡ 1 ,¡1),(0,1), and so on.

The tabled points are collinear and we can connect them with a

straight line.

We can use the techniques fromChapter 12to find the gradient

of the line. Using the points (0,1) and (1,3), the gradient is

y-step

x-step

or

rise

run

=^21 =2.

AXES INTERCEPTS

Thex-interceptof a line is the value ofxwhere the line meets thex-axis.

They-interceptof a line is the value ofywhere the line meets they-axis.

We can see that for the graph above, thex-intercept is¡^12 and they-intercept is 1.

B GRAPHING FROM A TABLE OF VALUES

-4

-2

2

4

6

-2 2

y

x

O

1

2

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Y:\HAESE\IGCSE01\IG01_14\299IGCSE01_14.CDR Friday, 17 October 2008 9:42:38 AM PETER