Question

How would you write an equation for a parallel and perpendicular line given 2 points?

Answer 1

you can find the slope of the line connecting the 2 points. with the slope, you can write equations for parallel and perpendicular lines.

parallel lines have the same slope
perpendicular lines have negative reciprocal slope (-1/m)

Answer 2

What about one point?

Answer 3

if you know the slope and you have one point, you can too