Page 132 - MAT KS3 Y8 Cambridge CheckPoint

13.1 Drawing graphs of equations

13.1 Drawing graphs of equations

Lines parallel to the x-axis have equations of the form y = a number. x = –6 y x = 12
12
Lines parallel to the y-axis have equations of the form x = a number.
8
This makes them easy to recognise and draw. y = 6
4
0 x
–12 –8 –4 4 8 12 16
In these examples, the number may be –4
referred to as a constant. –8 y = –8
–12
For more complicated equations it is helpful to start with a table
of values. The table will give the coordinates of points on the line. The equation of the x-axis is y = 0.
Then you can plot the points and join them to draw the graph.
The equation of the y-axis is x = 0.

Worked example 13.1
a Complete the table of values for y = 2x − 4.

x −2 −1 0 1 2 3 4
y −8 0 4
b Draw a graph of y = 2x − 4.

a If x = 3, y = 2 × 3 − 4 = 2
x −2 −1 0 1 2 3 4
If x = 1, y = 2 × 1 − 4 = −2
y −8 −6 −4 −2 0 2 4
If x = 0, y = 2 × 0 − 4 = −4
If x = −1, y = 2 × −1 − 4 = −6

b y Plot the points and use a ruler to draw a line through them all. It should be
4 a straight line. Extend the line to the end of the grid.
3
2
1
0 x
–2 –1 1 2 3 4
–1
–2
–3
–4
–5
–6
–7
–8

All the graphs in this unit are straight lines. If the points you plot are not in a straight line,
this shows you have made a mistake. Try to decide which point is incorrect and correct it.

130 13 Graphs