Perpendicular lines

The Maths Habit

  1. Gradient 3, crosses the y axis at −2. Write the equation.

    y = 3x − 2

  2. What is the gradient of y = 7 − 4x?

    −4

  3. Where does y = 12x + 6 cross the y axis?

    (0, 6)

Sam says any two straight lines that cross are perpendicular. Is Sam right?

No: they must cross at a right angle

Perpendicular
At right angles. The two gradients multiply to make −1.

Flip it and change the sign

2 −12

Flip it and change the sign

−3 13

Flip it and change the sign

14 −4

Perpendicular? Yes or no

y = 3x + 1  and  y = −13x + 4 Yes

  1. Find the gradient of a line perpendicular to y = 5x + 2.

    −15

  2. Find the gradient of a line perpendicular to y = −2x.

    12

  3. Find the gradient of a line perpendicular to y = 34x − 1.

    −43

Perpendicular to y = 4x − 1, through (8, 2).

gradient of the line given4
flip it and change the sign−14
put the point in to find c2=−14×8+ c
Answery = −14x + 4

Perpendicular to y = −3x + 2, through (3, 5).

gradient of the line given−3
flip it and change the sign13
put the point in to find c5=13×3+ c
Answery = 13x + 4

Perpendicular to y = 4x − 1, through (8, 2).

gradient of the line given4
flip it and change the sign−14
put the point in to find c2=−14×8+ c
Answery = −14x + 4

Perpendicular to y = 12x + 1, through (2, 1).

gradient of the line given12
flip it and change the sign−2
put the point in to find c1=−2×2+ c
Answery = −2x + 5

Perpendicular to y = 4x − 1, through (8, 2).

gradient of the line given4
flip it and change the sign−14
put the point in to find c2=−14×8+ c
Answery = −14x + 4

Perpendicular to y = 2x + 7, through (4, 1).

gradient of the line given2
flip it and change the sign−12
put the point in to find c1=−12×4+ c
Answery = −12x + 3

Perpendicular to y = 4x − 1, through (8, 2).

gradient of the line given4
flip it and change the sign−14
put the point in to find c2=−14×8+ c
Answery = −14x + 4

Perpendicular to y = −14x + 3, through (1, 6).

gradient of the line given−14
flip it and change the sign4
put the point in to find c6=4×1+ c
Answery = 4x + 2

Perpendicular to y = 4x − 1, through (8, 2).

gradient of the line given4
flip it and change the sign−14
put the point in to find c2=−14×8+ c
Answery = −14x + 4

Perpendicular to y = 23x − 5, through (6, 2).

gradient of the line given23
flip it and change the sign−32
put the point in to find c2=−32×6+ c
Answery = −32x + 11

Perpendicular lines worksheet, page 1

Answer sheet

  1. A is (0, 2) and B is (4, 4). Find the gradient of a line perpendicular to AB.

    −2

  2. Are y = 2x + 5 and 2y = −x + 6 perpendicular?

    Yes

  1. Find the gradient of a line perpendicular to y = 6x − 1.

    −16

  2. Find the line perpendicular to y = −5x + 2 through (10, 1).

    y = 15x − 1

  3. Are y = 3 − 2x and y = 12x + 4 perpendicular?

    Yes: −2 × 12 = −1
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