Two lines are parallel if they have the same gradent.
The lines y = 2x + 1 and y = 2x + 3 are parallel, because both have a gradient of 2.
Two lines are perpendicular if one is at right angles to another- in other words, if the two lines cross and the angle between the lines is 90 degrees.
If two lines are perpendicular, then their gradients will multiply together to give -1.
Find the equation of a line perpendicular to y = 3 – 5x.
This line has gradient -5. A perpendicular line will have to have a gradient of 1/5, because then (-5) × (1/5) = -1. Any line with gradient 1/5 will be perpendicular to our line, for example, y = (1/5)x.