Lines that are parallel have the same gradient (m)

Two perpendicular lines have gradients which multiple to be -1.

the gradient of y = 2x + 1 is 2. To find the number that can be multiplied with it to get -1, you find the negative reciprocal of 2 (flip it, then add a - if positive, or + if negative)
negative reciprocal of 2 (or 2/1, same thing) = -1/2
however negative reciprocal of -5 (or -5/1) = 1/5 (because negative and negative is positive)
example of a perpendicular line would be y = -1/2x + 6

To find the equation of a straight line (given two points), you use: y₂ - y₁ / x₁ - x₁ (= change in y / change in x) for the gradient.

Put the m into y = mx + c, then rearrange to find c

OR

Use the formula y - y₁ = m(x - x₁) where m is gradient, and x₁ and y₁ are one of the two points given.

	Created by Vanessa Andrews about 4 years ago

Year 7 Maths Slide Set on Spring Term 1, created by Vanessa Andrews on 11/02/2020.