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Identify Parallel Lines

In this worksheet, students will use y = mx+c to identify parallel lines.

'Identify Parallel Lines' worksheet

Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   Pearson Edexcel, OCR, Eduqas, AQA

Curriculum topic:   Algebra, Graphs of Equations and Functions

Curriculum subtopic:   Graphs, Straight Line Graphs

Difficulty level:  

Worksheet Overview

QUESTION 1 of 10

You can identify parallel lines by the fact that they are the same gradient.

 

y = 3x + 1 and y = 3x - 7 are parallel. They both have a gradient of 3.

 

y = 3x + 1 and y = 7 - 3x are not parallel. The first has a gradient of 3, whereas the second has a gradient of - 3.

 

You need to make sure that the equation of the line is in the form y = mx + c as this is the only way of finding what the gradient is. If the line has a different form, rearrange to y = mx + c. m represents the gradient of the line.

 

Example

Two lines have the equations y = 5x + 2 and 2y + 6 = 10x. Are these two lines parallel?

y = 5x + 2 is already in the correct form, so it can stay as it is. The gradient of this line is 5.

2y + 6 = 10x is not in the correct form, so we need to rearrange.

2y = 10x - 6

y = 5x - 3

The gradient of the second line is 5.

The gradients of both lines are 5, so yes, they are parallel.

Tick all the equations of the lines parallel to y = 5x - 1.

5y = x + 2

y = 5x + 3

3y = 15x - 9

2y = 5x + 6

Choose an equation of a line parallel to y = 2x + 3.

2y = 2x + 5

2x + 5y = 1

6y - 12 = 12x

2y = x + 12

Match the equations into pairs of parallel lines.

Column A

Column B

y = 0.5x + 3
y = 4x + 3
3y = 6 - 1.5x
2y = x + 7
y = 4x + 1
y = 4 - x
x + y = 5
y = 7 - 0.5x

One of the statements below is false. Pick the false statement.

The gradient of 5y - 3 = 4x is 4.

y = 4x + 7 is parallel to 2x - 0.5y = 3

2y + 3x = 3 and 2y + 5y = 3 are not parallel.

The gradient of 2y + 4x = 8 is -2.

Tick all the lines parallel to y = 1/3x + 7.

3y - x = 4

6y = 2x - 1

3y + 5 = x + 1

5 + 3y - x = 0

A line parallel to 7y - 49x = 63 will have a gradient of:

7x

49

7

-7

Here are four lines

Line 1: 4y = 3x + 5

Line 2: y = 3x - 2

Line 3: 5y - 15x = 1

Line 4: 3x + y = 1

Pick the correct statement.

Lines 1 and 2 are parallel.

Lines 2 and 3 are parallel.

Lines 1 and 4 are parallel.

Lines 3 and 4 are parallel.

Line 1 has an equation 3x + 5y = 17.

Line 2 is parallel to Line 1. What is the gradient of Line 2?

3x

-3/5

3/5x

3/5

A line with an equation ax + 3y - 11 = 0  is parallel to the line 6y + 2x + 1 = 0.

What is the value of a?

Which of the following lines is not parallel to 4x - 3y = 2?

0 = 8x - 6y + 9

8x - 6y = 7

4x = 3y - 1

3y + 4x = 2

  • Question 1

Tick all the equations of the lines parallel to y = 5x - 1.

CORRECT ANSWER
y = 5x + 3
3y = 15x - 9
EDDIE SAYS
y = 5x - 1 has a gradient of 5. There are two equations here with the same gradient: y = 5x + 3 and 3y = 15x - 9. The second equations can be rearranged to y = 5x - 3.
  • Question 2

Choose an equation of a line parallel to y = 2x + 3.

CORRECT ANSWER
6y - 12 = 12x
EDDIE SAYS
The line parallel to y = 2x + 3 is 6y - 12 = 12x. This is how you can rearrange it to show that the gradient is 2. 6y = 12x + 12 y = 2x + 2
  • Question 3

Match the equations into pairs of parallel lines.

CORRECT ANSWER

Column A

Column B

y = 0.5x + 3
2y = x + 7
3y = 6 - 1.5x
y = 7 - 0.5x
y = 4x + 1
y = 4x + 3
x + y = 5
y = 4 - x
EDDIE SAYS
Some of the equations need to rearranged into the form y=mx + c. 3y = 6 - 1.5x can be rearranged to y = 2 - 0.5x. The gradient of this line is -0.5. Remember about the minus! x + y = 5 can be rearranged to y = 5 - x. The gradient of this line is -1. Again, make sure you include the minus.
  • Question 4

One of the statements below is false. Pick the false statement.

CORRECT ANSWER
The gradient of 5y - 3 = 4x is 4.
EDDIE SAYS
The false statement is 'The gradient of 5y - 3 = 4x is 4'. If you rearrange 5y - 3 = 4x, you get y = 4/5x + 3/5. So the gradient here is 4/5, not 4!
  • Question 5

Tick all the lines parallel to y = 1/3x + 7.

CORRECT ANSWER
3y - x = 4
3y + 5 = x + 1
5 + 3y - x = 0
EDDIE SAYS
The gradient of the line y = 1/3x + 7 is 1/3. 3y - x = 4 rearranges to y = 1/3x + 4, so it's parallel. 3y + 5 = x + 1 rearranges to y = 1/3 x - 4/3, so it's also parallel. 5 + 3y - x = 0 rearranges to y = 1/3x - 5/3, so it'll be parallel as well.
  • Question 6

A line parallel to 7y - 49x = 63 will have a gradient of:

CORRECT ANSWER
7
EDDIE SAYS
Let's rearrange this equation! 7y - 49x = 63 7y = 63 + 49x y = 9 + 7x The gradient is just the number in front of x, so it's 7!
  • Question 7

Here are four lines

Line 1: 4y = 3x + 5

Line 2: y = 3x - 2

Line 3: 5y - 15x = 1

Line 4: 3x + y = 1

Pick the correct statement.

CORRECT ANSWER
Lines 2 and 3 are parallel.
EDDIE SAYS
Lines 2 and 3 are parallel. Their gradient is 3. Try rearranging the equation of line 3 to the form y=mx+c first.
  • Question 8

Line 1 has an equation 3x + 5y = 17.

Line 2 is parallel to Line 1. What is the gradient of Line 2?

CORRECT ANSWER
-3/5
EDDIE SAYS
Did you remember to rearrange the equation? 3x + 5y = 17 5y = 17 - 3x y = 17/5 - 3/5x The gradient is -3/5 (remember to include the sign!). So the gradient of Line 2 which is parallel must also be -3/5.
  • Question 9

A line with an equation ax + 3y - 11 = 0  is parallel to the line 6y + 2x + 1 = 0.

What is the value of a?

CORRECT ANSWER
1
EDDIE SAYS
First, let's rearrange 6y + 2x + 1 = 0. 6y = -2x - 1 y = -1/3 - 1/6. The gradient must be -1/3. Now, let's rearrange ax + 3y - 11 = 0 3y = - ax + 11 y = -a/3x + 11/3 -a/3 must be equal to -1/3. So the value of a is 1.
  • Question 10

Which of the following lines is not parallel to 4x - 3y = 2?

CORRECT ANSWER
3y + 4x = 2
EDDIE SAYS
The gradient of 4x - 3y = 2 is 4/3. 3y + 4x = 2 has a gradient of -4/3, so it\'s not parallel. All other lines have a gradient of 4/3.
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