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18.3 Drawing graphs

18.3 Drawing graphs

"is is the equation of a straight-line graph. y = −2x + 3

"e gradient of the straight line is −2.

You can write the equation in di#erent ways.
Change the order. y = 3 − 2x
Add 2x to both sides. y + 2x = 3
Change the order. 2x + y = 3

Subtract 3 from both sides. 2x + y − 3 = 0

"ese are all di#erent ways to write the equation of the line.

Worked example 18.3

The equation of a line is 2y − 3x + 4 = 0.
a Show that this is the equation of a straight line. b Find its gradient. c Draw a graph of the line.

a 2y + 4 = 3x Add 3x to both sides.
2y = 3x − 4 Subtract 4 from both sides.
y = 1.5x − 2 Divide both sides by 2.
This is the equation of a straight line. It is in the form y = mx + c.
b The gradient is 1.5. m is the gradient.

c y Make a table of values.
5 Three points are enough.
4 x 0 4 −2
3 1.5x − 2 −2 4 −5
2
1
0 x
–2 –1 1 2 3 4 5
–1
–2
–3
–4
–5

) Exercise 18.3

1 Write these equations in the form y = mx + c.
a x + y = 10 b 2x + y = 10 c x + 2y = 10 d 2x + 4y = 10

2 A graph has the equation 2x − y = 5.
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.

18 Graphs 18 Graphs 169