Page 133 - Mathematics Coursebook

13.3 Other straight lines

13.3 Other straight lines

You can use an equation to #nd pairs of values of x and y that obey the rule.

Remember that an equation is like a rule connecting x and y.
All the graphs in this unit
will be straight lines.
Look at the equation y = x + 2.
Choose any value for x and then work out the corresponding values y
of y. Each time you will get the coordinates of a point. 8
7

t If x = 4 then y = 4 + 2 = 6 "is gives the coordinates (4, 6). 6

t If x = 1 then y = 1 + 2 = 3 "is gives the coordinates (1, 3). 5

t If x = −3 then y = −3 + 2 = −1 "is gives the coordinates (−3, −1). 4
t If x = 0 then y = 0 + 2 = 2 "is gives the coordinates (0, 2). 3

2
If you plot these points, you can draw a straight line through them. 1

Any other points you #nd, using this equation, will be on the same –4 –3 –2 –1 0 1 2 3 4 x
line, y = x + 2. –1
If your line is not straight, check you have –2
worked out the coordinates correctly.

Worked example 13.3

a Complete this table of values for y = 5 − 3x.
b Use your table to draw the graph of y = 5 − 3x. x −2 −1 0 2 3
y 8 −2

x −2 −1 0 2 3 If x = −2 then y = 5 − 3 × −2 = 11 It is always helpful to
y 11 8 5 −1 −4 If x = 0 then y = 5 − 3 × 0 = 5 put the values in a
If x = 3 then y = 5 − 3 × 3 = −4
table, like this.
y
Think carefully about the numbers you put on the axes.
b 12 Think carefully about the numbers you put on the axes.

11 The x-axis must include −2 and 3. The y-axis must
10 include −4 and 11.
9 Make sure you can plot all fi ve points.
8 The points are in a straight line. Draw a line through all
7 the points.
6 Make the line as long as the grid allows.
5
4
3
2
1
0 x
–4 –3 –2 –1 –1 1 3 4 5
2
–2
–3
–4
–5

132 13 Graphs