Higher only · perpendicular lines
Perpendicular
gradients
multiply to −1.
flip it and
change the sign
lines that meet at 90° —
Perpendicular
gradients are negative reciprocals
m becomes −1 ÷ m
step 1 of 4
Flip, then change sign
1. Turn the gradient upside down.
2. Then change its sign.
✓ Check: 2 × −½ = −1
step 2 of 4
Find the new gradient
1. Read the gradient from y = mx + c.
2. Its negative reciprocal is −½.
✓ The + 5 does not matter
y = 2x + 5
gradient = 2
perpendicular: m = −12
step 3 of 4
Through a point: (4, 1)
1. Put x = 4 and y = 1 into the line.
2. Solve for c.
✓ c = 3
y = −12x + c
1 = −12 × 4 + c
1 = −2 + c
c = 3
step 4 of 4
Write the equation
1. Put m and c back into y = mx + c.
2. Works for any gradient and point.
✓ Parallel? Keep m the same instead
y = −12x + 3
2 × −12 = −1 perpendicular
perpendicular lines —
Perpendicular
gradients multiply to −1
Point
substitute it to find c
Rearrange to y = mx + c
before reading the gradient.
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