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18.3 Drawing graphs

3 A graph has the equation x + 2y + 4 = 0.
a Show that this is the equation of a straight line.
b Find the gradient of the line.
c Draw a graph of the line. y
10
4 a Show that the equation of this line is 2x + 3y = 24. 8
b Find the gradient of the line. 6

5 a Write each of these equations in the form y = mx + c. 4
i x − y + 6 = 0 ii 2x − 3y + 6 = 0 2
b Draw the graph of each line. 0 x
c Find the gradient of each line. –4 –2 2 4 6 8 10 12
–2
–4

6 Match each equation to the correct line. D y
a x + 2y = 8 10
b x − 2y = 8 8 A
c y + 2x = 8 6
d 2y − x = 8 C 4
A
2
B
0 x
–4 –2 2 4 6 8 10
–2 C
–4
B D
7 a Write x + 4y = 40 in the form y = mx + c. y
b Which line has the equation x + 4y = 40? 30
c Find the equations of the other two lines. A 20
B
10
C
0 x
–20 –10 10 20 30 40 50 60 70 80
–10
–20

8 a Rewrite these equations in the form y = mx + c.
i 20x = 2y + 15 ii x = 20y + 60
b Find the gradient of each line in part a. Choose a sensible scale for each axis.
c Draw the graph of each line.

9 The equation of line A is x = 20y. y
a Find the gradient of line A. Line B
b Find the coordinates of point P. P
c Find the equation of line B. Line A
0 x
–10 10 20 30 40 50

10 a Draw a graph of each of these lines. Use the same set of axes.
Your graphs must show where each line crosses the axes. Choose the same scale on each axis.
i 5x + 2y = 100 ii 2x + 5y = 100
b Find the gradient of each line.
c Where do the lines cross?

170 18 Graphs 18 Graphs