Parallel and perpendicular lines on a plane

This online calculator checks lines' slopes to see if they are parallel or perpendicular

Michele

Created: 2011-07-30 08:52:02, Last updated: 2020-11-09 16:15:56

The slope-intercept equation can define the line on a plane
$y=kx+b$

Suppose we have two lines with equations $y=k_1x+b_1$ and $y=k_2x+b_2$.

For lines to be parallel it is needed that
$k_1=k_2 , b_1 <> b_2$

For lines to be perpendicular it is needed that
$k_1k_2=-1$

This is quite easy for mental calculation, but lines also can be defined by more general form
$A_1x+B_1y+C_1=0$ and $A_2x+B_2y+C_2=0$

Then, for lines to be parallel it is needed that
$\frac{A_1}{A_2}=\frac{B_1}{B_2} <> \frac{C_1}{C_2}$

And for lines to be perpendicular it is needed that
$A_1A_2+B_1B_2=0$

So, the calculator below frees you from converting this to slope-intercept form and checks if lines are parallel or perpendicular

Parallel and Perpendicular Lines

The lines are parallel

The lines are perpendicular

URL copied to clipboard
PLANETCALC, Parallel and perpendicular lines on a plane