Parallel linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these best completes the definition of parallel: 'Two lines are parallel if they are straight lines which...'?

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.
Match the equation of each straight line to its gradient.

$y = 5x + 6$

⇔

gradient is 5 ✓

$y = 6x + 3$

⇔

gradient is 6 ✓

$y = 3 - 5x$

⇔

gradient is -5 ✓

$y = -(6 + 3x)$

⇔

gradient is -3 ✓

$y + 6x = 5$

⇔

gradient is -6 ✓

$2y = 6x + 5$

⇔

gradient is 3 ✓
The gradient of the line shown on this graph is ______.

'2' ✓
Which of these coordinates are on the line $y = -x - 5$ ?

(-10, 5) ✓

(-4, 1)

(-3, -2) ✓

(2, -7) ✓

(7, -2)
What is the gradient of the line with equation $3y + 4x - 8 = 0$ ?

$3\over 4$

$4\over 3$

$-{3\over 4}$

$-{4\over 3}$ ✓

$4$
A line passes through the points with coordinates (-3, 4) and (5, -12). The gradient of this line is ______.

'-2' ✓

Exit quiz

Five lines have been drawn on the same graph. Which of these lines is parallel to line A (black)?

line B (pink)

line C (blue) ✓

line D (purple)

line E (green)
Match each equation of a line to an equation of a line that is parallel to it.

$y = x + 4$

⇔

$y = x + 100$ ✓

$y = 2x - 3$

⇔

$y = 2x + 0.5$ ✓

$y = 3 - x$

⇔

$y = -x + {5\over 2}$ ✓

$y = 3x - 1$

⇔

$y = 4 + 3x$ ✓

$y = -2x + 1$

⇔

$y = 3 - 2x$ ✓
Which of these equations will produce a line that is parallel to the line with equation $5y - 2x = 15$ ?

$y = {2\over 5}x + 3$

$y = {5\over 2}x + 7$

$y = 8 - {2\over 5}x$

$5y = 2x + 5$ ✓

$8y + 20x = 40$
The line with equation $y =$ ______ $- 2x$ passes through the point (1, 4) and is parallel to the line $y = 7 - 2x$ .

'6' ✓
Which of these is the equation of the line which goes through the point (10, 20) and is parallel to the line $y = {5\over 2}x + 1$ ?

$y = {2\over 5}x + 4$

$y = {2\over 5}x + 16$

$y = {5\over 2}x - 5$ ✓

$y = {5\over 2}x + 10$

$y = 5x - 30$
The line L passes through the points with coordinates (3, 7) and (5, 10). Which of these lines are parallel to the line L?

A line passing through coordinates (2, 6) and (4, 9) ✓

A line passing through coordinates (-5, 1) and (-7, 4)

A line passing through coordinates (0, 1) and (6, 10) ✓

The line with equation $y = {3\over 2}x$ ✓

The line with equation $y ={2\over3} x$

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Lesson Details

Key learning points

Two lines are parallel if they are equidistant and never touch.
For linear graphs, the rate of change is constant.
If the gradients are the same then the linear graphs may be parallel.
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.