Parallel and perpendicular lines on a plane

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

The line on a plane can be defined by the slope-intercept equation

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

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 is it needed that

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

PLANETCALC, Parallel and Perpendicular Lines

Parallel and Perpendicular Lines

The lines are parallel
The lines are perpendicular