Calculadora online: Parallel and perpendicular lines on a plane

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

The lines are parallel

The lines are perpendicular

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