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WorkSHEET 14.1 Coordinates and linear graphs
Name: ___________________________ Fluency
1
Use the graph to answer the following
questions.
(a) Who is the shortest?
(b) Who is the tallest?
(c) Is the heaviest person the tallest?
(d) Who is the lightest?
Answers:
(a) Beth
(b) Sam
(c) No
(d) Ken
2
Use the graph to answer the following
questions.
(a) In which section did the temperature stay
the same?
(b) In which sections did the temperature
increase?
(c) In which sections did the temperature
decrease?
Answers:
(a) C
(b) A, B
(c) D, E
3 Place the following points on a Cartesian plane.
A (0, 2)
B (2, 2)
C (3, 0)
D (1, 5)
E (2, 4)
Answer:
WorkSHEET 14.1 Coordinates and linear graphs
4 Write down the coordinates of the points A to I
shown on the Cartesian plane below.
Answers:
A (1, 0)
B (4, 4)
C (2, 2)
D (2, 4)
E (1, 0)
F (0, 3)
G (5, 4)
H (4, 3)
I (3, 3)
5 (a) Plot the following points on a Cartesian
plane.
96303
21012
y
x
(b) Plot the following points on a Cartesian
plane.
31135
21012
y
x
(c) Do the points in parts (a) and (b) form a
linear graph?
Answers:
(a)
(b)
(c) Yes
6 Would each of the following sets of points
form a linear graph?
(a) (4, 2) (3, 3) (2, 1) (1, 0) (0, 4)
(b) (4, 9) (3, 11) (2, 15) (1, 16) (0, 20)
(c) (4, 24) (3, 18) (2, 12) (1, 6)
(0, 0)
Answers:
(a) No
(b) No
(c) Yes
WorkSHEET 14.1 Coordinates and linear graphs
7 Write the next point in the linear pattern for the
following.
(a) (2, 1) (1 2) (0, 0) (1, 2) (2, 4)
(b) (2, 4) ( 1, 2) (0, 0) (1, 2) (2, 4)
(c) (2, 5) (1, 0) (0, 5) (1, 10) (2, 15)
Answers:
(a) (3, 6)
(b) (3, 6)
(c) (3, 20)
Understanding
8 Draw a Cartesian plane with x-axis from
5 to 5 and y-axis from 5 to 5. Plot the
following points and connect them using the
following directions.
Start (4, 5) (4, 5) (4, 5) (4, 5) (4, 5) Stop
Start (3, 0) (3, 1) (2, 1) (2, 0) (–3, 0) Stop
Start (2, 0) (2, 1) (3, 1) (3, 0) (2, 0) Stop
Start (2, 3) (2, 4) (2, 4) (2, 3) Stop
Answer:
9 (a) Plot the following points on a Cartesian
plane.
2
123
2
13
5201
y
x
(b) Do the points form a linear pattern?
Answers:
(a)
(b) Yes, a linear pattern
10 Write down the next point for the following
linear patterns.
(a) (0, 2
12 ) (1, 4) (2,
2
15 ) (3, 7)
(b) (0, 2
15 ) (2,
2
17 ) (4,
2
19 ) (6, 11
2
1)
(c) (2, 2
11 ) (
2
11 , 1) (1,
2
1 )
(2
1 , 0)
Answers:
(a) (4, 1
82
)
(b) (8, 1
132
)
(c) (0, 1
2)
WorkSHEET 14.1 Coordinates and linear graphs
WorkSHEET 14.2 Coordinates and linear graphs
Name: ___________________________ Fluency
8 Find the rule for each of the following.
63036
21012(a)
y
x
76543
21012(b)
y
x
Answers:
(a) 3y x
(b) 5y x
9 Are the following statements true or false?
(a) The rule for the table of values below is
y = x 2.
01234
21012
y
x
(b) The rule for the table of values below is
y = 2x + 1.
31024
21012
y
x
Answers:
(a) True
(b) False
WorkSHEET 14.1 Coordinates and linear graphs
10 Complete the tables of values and then plot the
graphs on Cartesian planes.
(a) y = x 3
y
x 3210123
(b) y = 4x
y
x 3210123
Answers:
(a) y = x 3
0123456
3210123
y
x
(b) y = 4x
128404812
3210123
y
x
WorkSHEET 14.1 Coordinates and linear graphs
11 Choose the correct answer.
The table of values for 43 xy is shown by:
A 54321
21012
y
x
B 107412
21012
y
x
C 108642
21012
y
x
D 97531
21012
y
x
E 117415
21012
y
x
Answer: B
WorkSHEET 14.1 Coordinates and linear graphs
12 Make a table of values for 3 < x < 3 and plot a
graph for each of the following relations.
(a) xy 2
(b) 3 xy
(c) 52 xy
Answers:
(a) y = 2x
6420246
3210123
y
x
(b) y = x + 3
6543210
3210123
y
x
(c) y = 2x + 5
11357911
3210123
y
x
WorkSHEET 14.1 Coordinates and linear graphs
13 Find the gradient of the following linear graphs.
(a)
(b)
Answers:
(a) m = 2
(b) m = 4
14 Find m and c for each of the following.
(a)
(b)
Answers:
(a) m = 3 and c = 0
(b) m =2
3 and c = 3
WorkSHEET 14.1 Coordinates and linear graphs
15
Choose the correct answer.
The gradient and y-intercept, respectively, of
the graph above is:
A m = 3, c = 6
B m = 2, c = 6
C m = 2, c = 6
D m = 6, c = 3
E m = 3, c = 6
Answer: E
16 State the gradient and y-intercept of each of the
following linear graphs.
(a) 5 xy
(b) 48 xy
Answers:
(a) m = 1 and c = 5
(b) m = 8 and c = 4
17 Sketch the following graphs using the gradient
and y-intercept method.
(a) 2 xy
(b) 13 xy
Answers:
(a)
(b)
WorkSHEET 14.1 Coordinates and linear graphs
18 Sketch the following graphs using the x- and
y-intercept method.
(a) 3 xy
(b) 5 xy
Answers:
(a)
(c)
19 Draw graphs for each of the following rules
and state the value of the gradient in each case.
(a) y = 4
(b) x = 3
Answers:
(a)
m = 0
(b)
Gradient is undefined.
WorkSHEET 14.1 Coordinates and linear graphs
Understanding
20 State the rule for each of the following linear
graphs.
(a)
(b)
Answers:
(a) Gradient, m = rise
run
Gradient, m = 1
1
Gradient, m = 1
c = 0
y = mx + c
y = 1 x + 0
y = x
(b) Gradient, m = rise
run
Gradient, m = 4
4
Gradient, m = 1
c = 4
y = mx + c
y = 1 x + 4
y = x + 4
21 Choose the correct answer.
The gradient and y-intercept of the graph given
by 1242 xy is:
A m = 2, c = 6
B m = 2, c = 6
C m = 4, c = 12
D m = 4, c = 12
E m = 4, c = 6
Answer: B
2 4 12y x
2y = 4x + 12
y = 2x + 6
y = mx + c
m = 2, c = 6
WorkSHEET 14.1 Coordinates and linear graphs
22 Are the following statements true or false?
(a) The x- and y-intercepts for the linear
graph 4 xy are 4 and 4.
(b) The x- and y-intercepts for the linear
graph 4 xy are 4 and 4.
Answers:
(a) y = x + 4
x int, y = 0
0 = x + 4
0 4 = x + 4 4
x = 4
y int, x = 0
y = 0 + 4
y = 4
False
(b) y = x 4
x int, y = 0
0 = x 4
0 + 4 = x 4 + 4
x = 4
y int, x = 0
y = 0 4
y = 4
True
23 The point with coordinates (3, 5) lies on the
line with equation:
A 2x – y = 1
B x + y = 8
C y = x + 8
D y – x = 8
E 2x + y = 1
Answers: C
5 = 3 + 8
WorkSHEET 14.1 Coordinates and linear graphs
24 The x-intercept for a linear graph is 4 and the
y-intercept is 2.
(a) Sketch the graph.
(b) Find the equation of the linear graph.
Answers:
(a)
(b) m = rise
run c = 2
m = 2
4
m = 1
2
12
2
y mx c
x
25 Leo used matchsticks to build a model fence.
F represents the number of sections of fencing,
and M represents the number of matchsticks.
His results are shown in the table below:
1 2 3 4 5
6 11 16 21 26
F
M
(a) Plot these points on a Cartesian plane.
(b) State the independent and dependent
variables.
(c) Is there a linear relationship?
(d) Find m and c.
(e) Use m and c to form a linear equation.
Answers:
(a)
(b) F (sections of fencing) represents the
independent variable.
M (number of matchsticks) represents the
dependent variable.
(c) Yes
(d) m = 5 and c = 1
(e) y = mx + c
5 1M F
WorkSHEET 14.1 Coordinates and linear graphs
26 Judy swims each lap of a 50-m pool in 2 min.
(a) Copy and complete the following table.
Time (min) 2 4 6 8 10
Distance (m) 50
(b) Plot these points on a Cartesian plane.
(c) Do the points form a linear relationship?
(d) Find m and c.
(e) Use m and c to form a linear equation.
Answers:
(a)
Time (min) 2 4 6 8 10
Distance (m) 50 100 150 200 250
(b)
(c) Yes
(d) m = 25 and c = 0
(e) y = mx + c
D = 25T