Parallel lines have the same gradient. y = 2x + 1 and y = 2x − 7 are parallel because both have gradient 2.
Perpendicular lines meet at a right angle. Their gradients multiply to −1, so one gradient is the negative reciprocal of the other. A line perpendicular to y = 2x + 1 has gradient −1/2. A line perpendicular to y = −(4/3)x + 7 has gradient 3/4.
To find the full equation, use the new gradient with a point the line passes through, then solve for c.
Worked example
Find the gradient of a line perpendicular to y = −5x + 2.
- The gradient is −5.
- Negative reciprocal: flip and change the sign.
Answer:1/5
Key words
- parallel
- same gradient, never meet
- perpendicular
- meet at 90°
- negative reciprocal
- flip the fraction and change its sign
Practise this
New questions every time.
Common Core-referenced: HSG-GPE.B.5