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End-of-unit review

End-of-unit review

1 Work out the gradient of each line on the graph. a b y
4
3
2 a
1
0 x
–4 –3 –2 –1 1 2 3 4
–1 c
–2
b –3

c –4
2 Find the gradient of a straight line between:
a (0, 0) and (10, 2) b (0, 6) and (6, −6) c (5, 2) and (−3, −2).
3 Find the gradients of the lines with these equations.
a y = 4x − 5 b y = 4 − 5x c 2 + 3x = y d x + y = 20
4 Write each formula in the form y = mx + c.
a 2x + y = 4 b x + 4y = 2 c 2y + 4 = x d 3(x − y) = 2

5 These are the equations of three straight lines. Find the gradient of each one.
1
a 2x + y = 9 b x = 2y + 4 c 1 y = x − 12
4 2
6 These are the equations of five straight lines.
A: y + 2x = 5 B: y + 5 = 2x C: 2y = 7 − 4x D: 2x + 2y = 5 E: 2x − y = 1
Which lines are parallel?

7 Use the graph to find solutions to each pair of simultaneous y
equations. 4
a x + 2y = 5 and 3x + y = 13 3
b y + 20 = 3x and x + 2y = 5 2
c 3x + y = 13 and y + 20 = 3x 1
8 a Draw graphs of the straight lines with these equations. –2 –1 0 1 2 3 4 5 6 7 8 x
Draw both lines on the same grid. –1
–2
i y = 3x + 7 ii 2y + x = 2
b Use your graph to find approximate solutions to these –3
simultaneous equations. –4
y = 3x + 7 and 2y + x = 2

9 The cost of hiring a car is $40 plus a charge of $30 per day.
a How much will it cost to hire a car for two days?
b Find a formula to show the cost (c), in dollars, of hiring a car for d days.
c Draw a graph to show the cost of hiring a car.
d A driver pays $220 to hire a car. Use the graph to find the number of days she had the car.

10 The exchange rate between Hong Kong dollars (HK$) and Pakistani rupees (PR) is HK$1 = 12.2 PR.
a Draw a graph to show the exchange rate. Put HK$ on the horizontal axis. Go up to 100 HK$.
b Use the graph to convert 500 PR to HK$.
c Use a calculation to get a more accurate answer to part b.

176 18 Graphs 18 Graphs