New
New
Year 10
Higher

# Parallel linear graphs

I can identify, from their equations or graphs, whether two lines are parallel.

New
New
Year 10
Higher

# Parallel linear graphs

I can identify, from their equations or graphs, whether two lines are parallel.

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## Lesson details

### Key learning points

1. Two lines are parallel if they are equidistant and never touch.
2. For linear graphs, the rate of change is constant.
3. If the gradients are the same then the linear graphs may be parallel.
4. The y-intercepts must be different, otherwise the lines are the same.

### Common misconception

Lines are parallel if they have the same gradient.

Lines are parallel if they have the same gradient and different y-intercepts. Two lines are parallel if they are straight lines that are always the same non-zero distance apart.

### Keywords

• Gradient - The gradient is a measure of how steep a line is. It is calculated by finding the rate of change in the y-direction with respect to the positive x-direction.

• Intercept - An intercept is the coordinate where a line or curve meets a given axis.

• Parallel - Two lines are parallel if they are straight lines that are always the same (non-zero) distance apart.

Pupils could use Desmos to explore which pairs of equations produce parallel lines when equations are not in the form y = mx + c
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Which of these best completes the definition of parallel: 'Two lines are parallel if they are straight lines which...'?
Correct answer: are always the same distance apart.
are the same length.
cross the $$y$$-axis at the same point.
have the same equation.
intersect at right angles.
Q2.
Match the equation of each straight line to its gradient.
Correct Answer:$$y = 5x + 6$$,gradient is 5

Correct Answer:$$y = 6x + 3$$,gradient is 6

Correct Answer:$$y = 3 - 5x$$,gradient is -5

Correct Answer:$$y = -(6 + 3x)$$,gradient is -3

Correct Answer:$$y + 6x = 5$$,gradient is -6

Correct Answer:$$2y = 6x + 5$$,gradient is 3

Q3.
The gradient of the line shown on this graph is .
Q4.
Which of these coordinates are on the line $$y = -x - 5$$ ?
(-4, 1)
(7, -2)
Q5.
What is the gradient of the line with equation $$3y + 4x - 8 = 0$$ ?
$$3\over 4$$
$$4\over 3$$
$$-{3\over 4}$$
Correct answer: $$-{4\over 3}$$
$$4$$
Q6.
A line passes through the points with coordinates (-3, 4) and (5, -12). The gradient of this line is .
Correct Answer: -2, negative 2, negative two

## Exit quiz

### 6 Questions

Q1.
Five lines have been drawn on the same graph. Which of these lines is parallel to line A (black)?
line B (pink)
line D (purple)
line E (green)
Q2.
Match each equation of a line to an equation of a line that is parallel to it.
Correct Answer:$$y = x + 4$$,$$y = x + 100$$

$$y = x + 100$$

Correct Answer:$$y = 2x - 3$$,$$y = 2x + 0.5$$

$$y = 2x + 0.5$$

Correct Answer:$$y = 3 - x$$,$$y = -x + {5\over 2}$$

$$y = -x + {5\over 2}$$

Correct Answer:$$y = 3x - 1$$,$$y = 4 + 3x$$

$$y = 4 + 3x$$

Correct Answer:$$y = -2x + 1$$,$$y = 3 - 2x$$

$$y = 3 - 2x$$

Q3.
Which of these equations will produce a line that is parallel to the line with equation $$5y - 2x = 15$$ ?
$$y = {2\over 5}x + 3$$
$$y = {5\over 2}x + 7$$
$$y = 8 - {2\over 5}x$$
Correct answer: $$5y = 2x + 5$$
$$8y + 20x = 40$$
Q4.
The line with equation $$y =$$ $$- 2x$$ passes through the point (1, 4) and is parallel to the line $$y = 7 - 2x$$.
Q5.
Which of these is the equation of the line which goes through the point (10, 20) and is parallel to the line $$y = {5\over 2}x + 1$$?
$$y = {2\over 5}x + 4$$
$$y = {2\over 5}x + 16$$
Correct answer: $$y = {5\over 2}x - 5$$
$$y = {5\over 2}x + 10$$
$$y = 5x - 30$$
Q6.
The line L passes through the points with coordinates (3, 7) and (5, 10). Which of these lines are parallel to the line L?
Correct answer: A line passing through coordinates (2, 6) and (4, 9)
A line passing through coordinates (-5, 1) and (-7, 4)
Correct answer: A line passing through coordinates (0, 1) and (6, 10)
Correct answer: The line with equation $$y = {3\over 2}x$$
The line with equation $$y ={2\over3} x$$