How can you find the equation of a line that is parallel / perpendicular to a given line

In order to find an equation of a line that is either parallel or perpendicular to a given line, you only need to look at the slopes. The slope of parallel lines are always going to be the same. This means when you solve for y, you will see the same coefficient of x.

Perpendicular lines will have opposite and reciprocal slopes. This means you can negate one of them and then flip the fraction and the result will be the perpendicular slope.