Cambridge International Mathematics

300 Straight lines (Chapter 14)

Example 1 Self Tutor

Consider the equation y=x¡ 2.

a Construct a table of values using x=¡ 3 ,¡ 2 ,¡ 1 , 0 , 1 , 2 and 3.

b Draw the graph of y=x¡ 2 :

c Find the gradient and axes intercepts of the line.

a x ¡ 3 ¡ 2 ¡ 1 0 1 2 3

y ¡ 5 ¡ 4 ¡ 3 ¡ 2 ¡ 1 0 1

b

c Using the points (0,¡2) and (2,0),

the gradient=

y-step

x-step

=

2

2

=1.

Thex-intercept is 2.

They-intercept is¡ 2.

EXERCISE 14B

1 For the following equations: i Construct a table of values for values ofxfrom¡ 3 to 3.

ii Plot the graph of the line.

iii Find the gradient and axes intercepts of the line.

a y=x b y=3x c y=^13 x d y=¡ 3 x

e y=2x+1 f y=¡ 2 x+1 g y=^12 x+3 h y=¡^12 x+3

2 Arrange the graphs1a,1band1cin order of steepness. What part of the equation controls the degree

of steepness of a line?

3 Compare the graphs of1band1d. What part of the equation controls whether the graph is forward

sloping or backward sloping?

4 Compare the graphs of1b,1eand1g. What part of the equation controls where the graph cuts the

y-axis?

Discovery 2 Graphs of the form y=mx+#endboxedheadingc

What to do:

1 On the same set of axes graph the family of lines of the form y=mx:

a where m=1, 2 , 4 ,^12 ,^15 b where m=¡ 1 ,¡ 2 ,¡ 4 ,¡^12 ,¡^15

2 What are the gradients of the lines in question 1?

3 What is your interpretation ofmin the equation y=mx?

4 On the same set of axes, graph the family of lines of the form y=2x+c where c=0, 2 , 4 ,

¡ 1 ,¡ 3 :

5 What is your interpretation ofcfor the equation y=2x+c?

GRAPHING

PACKAGE

-4

-2

-2 2

y

O x

2

2

The use of a graphics calculator or suitable graphing package is recommended for this Discovery.

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Y:\HAESE\IGCSE01\IG01_14\300IGCSE01_14.CDR Wednesday, 29 October 2008 4:13:12 PM PETER