worksheet 14.1 coordinates and linear graphs name:

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:


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


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)



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


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


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


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


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


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)


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.


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


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


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


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

worksheet 14.1 coordinates and linear graphs name:

Documents