Identifying perpendicular linear graphs | Maths | Quizalize & Oak National Academy

Starter quiz

Which of these show two lines which are perpendicular?
What is the gradient of this line?

$1\over 3$

$2\over 5$ ✓

$2\over 3$

$3\over 2$

$5\over 2$
Which of these values is the reciprocal of 4?

$-4$

$1\over 4$ ✓

$0.4$

$2$

$10\over 4$
Which of these coordinates lie on the line $x = 4.5$ ?

(0, 0)

(2.5, 4.5)

(3, 1.5)

(4.5, 7) ✓

(5, -0.5)
Which of these lines are parallel to the line with equation $2y-x = 5$ ?

$4y - 2x = 5$ ✓

$y = 2x + 8$

$y = {1\over 2}x - 1$ ✓

$y = 10-{1\over 2}x$

$6y - 4x = 3$
A line has gradient 4 and passes through the coordinate (3, 9). What is the equation of the line?

$y = 21 - 4x$

$y = 3x$

$y = 4x - 3$ ✓

$y = 4x$

$y = 4x + 9$

Match each number to its negative reciprocal.

$-3$

⇔

$1\over 3$ ✓

$1$

⇔

$-1$ ✓

$7$

⇔

$-{1\over 7}$ ✓

$-{4\over 5}$

⇔

$5\over 4$ ✓

$-{5\over 4}$

⇔

$4\over 5$ ✓

$1\over 7$

⇔

$-7$ ✓
Select the equation of a line perpendicular to the line with equation $y = {1\over 2}x$ .

$y = {1\over 4} x$

$y = 5 - {1\over 2}x$

$y = {1\over 2}x + 4$

$y = 2x + 1$

$y = 4 - 2x$ ✓
Which of these are equations of a line perpendicular to the line with equation $3y = 2x + 6$ ?

$y = {2\over 3}x +1$

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

$y = 3 - {1\over 2}x$

$y = 4 - {3\over 2}x$ ✓

$y = {1\over 2}x + 5$
Which of these are equations for lines which are perpendicular to the line with equation $y + 2.5x = 0$ ?

$y = {2\over 5}x +3$ ✓

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

$y = 5.2x + 3$

$2y + 5x = 3$

$5y = 2x + 3$ ✓
Which is the equation of the line which passes through the point (3, -1) and is perpendicular to the line with equation $y =2-{1\over 3}x$ ?

$y = -3x + 8$

$y = {1\over 3}x -2$

$y = {1\over 3}x -4$

$y = 3x - 4$

$y = 3x - 10$ ✓
Which of these are equations for lines which are perpendicular to the line with equation $y = {1\over\sqrt{20}}x$ ?

$y = 4 + \sqrt{20}x$

$y = 4 - \sqrt{20}x$ ✓

$y = 4\sqrt{5} x + 4$

$y = 4-2\sqrt{5} x$ ✓

$y = 4-4\sqrt{5} x$

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If two equations are written in the form y = mx + c then you can identify if they are perpendicular.
If the equations are not in that form, you can rearrange them to be.
From their graphs, you can identify whether two lines are perpendicular.

The gradients of two perpendicular lines are a number and its reciprocal.

In order for two lines to be perpendicular, the two gradients cannot have the same sign. Therefore it is a number and its negative reciprocal.

Perpendicular - Two lines are perpendicular if they meet at right angles.
Irrational number - An irrational number is one that cannot be written in the form a/b where a and b are integers and b is not equal to 0
Surd - A surd is an irrational number expressed as the root of a rational number.
Radical - The root sign is the radical symbol.