Mathematics: Gradient of Parallel and Perpendicular Lines
“Parallel lines have the same gradient”
Remember the form y=ax+b, where “a” is the gradient?
The gradient here is the same; it’s just the value of “b”, the y intercept that is different.
The rule to learn here is that for two functions y=ax+b and y1 = a1x1 +b1, a=a1
The actual functions here are : 2x+2 and 2x+5.
As you can see, the two values of “a” are the same but the values of “b” are different.
If you want to calculate the perpendicular of the gradient, simply remember this:
For the linear function y= ax+b, a*a1 (where a1 is the gradient of the perpendicular) = -1
So:
a * a1 = -1
We can rearrange this to get:
a1 = -1/ a
So for the function y= 2x+2, the gradient of the perpendicular line is:
a1 = -1/2
