Cambridge Additional Mathematics

Straight line graphs (Chapter 7) 187

EXERCISE 7C

1 Find the points where the line x¡ 2 y=3intersects the curve x^2 +y^2 =5.

2 The line x+y=7meets the curve x^2 +y^2 =29at A and B. Find the distance between A and B.

3 The line 2 x+y=5meets the curve x^2 +y^2 =10at P and Q. Find the equation of the perpendicular

bisector of PQ.

4 Find the points where the line x¡ 2 y=4intersects the curve 3 x^2 +y^2 +xy+3y=8.

5 The liney=2x+1meets the curvex^2 +y^2 +xy+16x=29at P and Q. Find the distance between

P and Q.

6 The line 3 x+y=1intersects the curve 2 x^2 +y^2 +5xy¡ 7 x=¡ 31 at A and B. Find the equation

of the perpendicular bisector of AB.

7 Find the points where the line x¡ 2 y=6intersects the curve^4

x

¡^1

y

=2.

8 The line 3 x+2y=12intersects the curve

4

x

+

3

y

=3at P and Q. Find the midpoint of PQ.

Even ifxandyare not linearly related, it is sometimes still possible to use a straight line graph to display

the relationship. We do this by changing the variables on the axes.

For example, consider the relationship y=2x^2 +1.

xandyare not linearly related, butx^2 andyarelinearly related

since y=2(x^2 )+1.

We can use a table of values to plotyagainstx^2 :

x 0 1 2

x^2014

y 1 3 9

The graph ofyagainstx^2 is a straight line with gradient 2 and

y-intercept 1.

Click on the icon to view a demonstration of how the two graphs are related.

Observe that for the graph ofyagainstx^2 , the line terminates at (0,1), since x^2 > 0 for

allx. We need to be careful with the domain and range when we transform relationships.

TRANSFORMING RELATIONSHIPS

straight line form D Transforming relationships to

D

DEMO

y

O x

(0 1),

(1 3),

(2 9),

y=2x +1 2

y

O x 2

(0 1),

(1 3),

(4 9),

4037 Cambridge

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Y:\HAESE\CAM4037\CamAdd_07\187CamAdd_07.cdr Friday, 20 December 2013 3:33:12 PM BRIAN