Question

How do you know when two lines are parallel $?$

Answer 1

Finding whether two lines are parallel or not , we must compare their slopes:

If the two lines are parallel then their slopes are equal.

Suppose the line are $2x-3y=4$, $2x-3y=18$

To check whether they are parallel or not,

In general, a line in the form

$Ax+By=C$has a slope of $-\frac{\mathbf{A}}{\mathbf{B}}$,

On comparing, both the lines have slope equal,

$\frac{\mathbf{2}}{\mathbf{3}}\mathbf{=}\frac{\mathbf{2}}{\mathbf{3}}$

Hence, the given lines are parallel.