Sec 2 G1 Maths Linear graphs worksheet with answers

A free Sec 2 G1 Maths worksheet on linear graphs: 7 questions, 30 marks, short questions first and then structured ones, in the school exam style. The answers and full worked solutions are on the last page.

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Sec 2 G1 Maths worksheet: Linear graphs

Total: 30 marksSuggested time: 50 minutes

Name: ______________________________Class: ____________ Date: ____________

Answer all questions. Show all your working. Give non-exact answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless the question says otherwise.

Section A

Which point has coordinates

(2, 4)

Answer[1]

State whether the gradient of the line shown is positive, negative, zero or not defined.

Answer[1]

ABCD

is a parallelogram. The points

A

B

and

C

are shown. Find the coordinates of

D

Answer[2]

(a)Complete the table of values for

y = 4x + 1

Answer (a)[3]

(b)Complete the table of values for

4x - y = -4

Answer (b)[3]

(a)Complete the table of values for

4x + 2y = 8

Answer (a)[3]

(b)Complete the table of values for

2x + 2y = 4

Answer (b)[3]

Section B

(a)State whether the gradient of the line shown is positive, negative, zero or not defined.

Answer (a)[1]

(b)(i)Complete the table of values for

y = x - 4

Answer (b)(i)[3]

(b)(ii)Complete the table of values for

y = 4x + 6

Answer (b)(ii)[3]

(a)Write down the coordinates of the point

E

Answer (a)[2]

(b)The line passes through the points

A

and

B

shown. Find its gradient.

Answer (b)[2]

(c)Complete the table of values for

y = 3x - 5

Answer (c)[3]

END OF PAPER

Answers and worked solutions

Question 1

Answer: B[1]

Go across

2

on the

x

-axis, then up

4

\text{B}

Question 2

Answer: POSITIVE[1]

The line goes up from left to right.So the gradient is positive.

Question 3

Answer: So

D(-3, 3)

.[2]

Across:

-1 - (-3) = 2

Up:

3 - (-3) = 6

x = -3

y = 3

D(-3, 3)

Question 4

(a)Answer:

y = 9

[3]

When

x = -2

y = 4(-2) + 1

y = -7

When

x = 1

y = 4(1) + 1

y = 5

When

x = 2

y = 4(2) + 1

y = 9

(b)Answer:

y = 8

[3]

-y = -4x - 4

y = 4x + 4

When

x = -1

y = 4(-1) + 4

y = 0

When

x = 0

y = 4(0) + 4

y = 4

When

x = 1

y = 4(1) + 4

y = 8

Question 5

(a)Answer:

y = -2

[3]

2y = -4x + 8

y = -2x + 4

When

x = -2

y = -2(-2) + 4

y = 8

When

x = 1

y = -2(1) + 4

y = 2

When

x = 3

y = -2(3) + 4

y = -2

(b)Answer:

y = -1

[3]

2y = -2x + 4

y = -x + 2

When

x = -2

y = -(-2) + 2

y = 4

When

x = -1

y = -(-1) + 2

y = 3

When

x = 3

y = -(3) + 2

y = -1

Question 6

(a)Answer: NEGATIVE[1]

The line goes down from left to right.So the gradient is negative.

(b)(i)Answer:

y = -2

[3]

When

x = -2

y = (-2) - 4

y = -6

When

x = -1

y = (-1) - 4

y = -5

When

x = 2

y = (2) - 4

y = -2

(b)(ii)Answer:

y = 22

[3]

When

x = -1

y = 4(-1) + 6

y = 2

When

x = 3

y = 4(3) + 6

y = 18

When

x = 4

y = 4(4) + 6

y = 22

Question 7

(a)Answer: So

E(-3, 2)

.[2]

x = -3

y = 2

E(-3, 2)

(b)Answer:

m = -1

[2]

A(-1, 0)

and

B(4, -5)

Rise:

-5 - 0 = -5

Run:

4 - (-1) = 5

m = \dfrac{-5}{5}

m = -1

(c)Answer:

y = 1

[3]

When

x = -1

y = 3(-1) - 5

y = -8

When

x = 0

y = 3(0) - 5

y = -5

When

x = 2

y = 3(2) - 5

y = 1

Sec 2 G1 Maths Linear graphs worksheet with answers

In the print window, choose Save as PDF to download it.

Or practise it online with step-by-step help when you get one wrong.

Section B

(a)State whether the gradient of the line shown is positive, negative, zero or not defined.

Answer (a)[1]

(b)(i)Complete the table of values for

y = x - 4

Answer (b)(i)[3]

(b)(ii)Complete the table of values for

y = 4x + 6

Answer (b)(ii)[3]

Answers and worked solutions

Question 1

Answer: B[1]

Go across

2

on the

x

-axis, then up

4

\text{B}

Question 2

Answer: POSITIVE[1]

The line goes up from left to right.So the gradient is positive.

Question 3

Answer: So

D(-3, 3)

.[2]

Across:

-1 - (-3) = 2

Up:

3 - (-3) = 6

x = -3

y = 3

D(-3, 3)

Question 4

(a)Answer:

y = 9

[3]

When

x = -2

y = 4(-2) + 1

y = -7

When

x = 1

y = 4(1) + 1

y = 5

When

x = 2

y = 4(2) + 1

y = 9

(b)Answer:

y = 8

[3]

-y = -4x - 4

y = 4x + 4

When

x = -1

y = 4(-1) + 4

y = 0

When

x = 0

y = 4(0) + 4

y = 4

When

x = 1

y = 4(1) + 4

y = 8

Question 5

(a)Answer:

y = -2

[3]

2y = -4x + 8

y = -2x + 4

When

x = -2

y = -2(-2) + 4

y = 8

When

x = 1

y = -2(1) + 4

y = 2

When

x = 3

y = -2(3) + 4

y = -2

(b)Answer:

y = -1

[3]

2y = -2x + 4

y = -x + 2

When

x = -2

y = -(-2) + 2

y = 4

When

x = -1

y = -(-1) + 2

y = 3

When

x = 3

y = -(3) + 2

y = -1

Question 6

(a)Answer: NEGATIVE[1]

The line goes down from left to right.So the gradient is negative.

(b)(i)Answer:

y = -2

[3]

When

x = -2

y = (-2) - 4

y = -6

When

x = -1

y = (-1) - 4

y = -5

When

x = 2

y = (2) - 4

y = -2

(b)(ii)Answer:

y = 22

[3]

When

x = -1

y = 4(-1) + 6

y = 2

When

x = 3

y = 4(3) + 6

y = 18

When

x = 4

y = 4(4) + 6

y = 22

Question 7

(a)Answer: So

E(-3, 2)

.[2]

x = -3

y = 2

E(-3, 2)

(b)Answer:

m = -1

[2]

A(-1, 0)

and

B(4, -5)

Rise:

-5 - 0 = -5

Run:

4 - (-1) = 5

m = \dfrac{-5}{5}

m = -1

(c)Answer:

y = 1

[3]

When

x = -1

y = 3(-1) - 5

y = -8

When

x = 0

y = 3(0) - 5

y = -5

When

x = 2

y = 3(2) - 5

y = 1