How would you determine whether two lines are parallel by looking at the equations of the lines in standard form.
I found a trick on one site saying that the slope of a standard equation (Ax + By = C) is equal to -A/B. Is this true? Does anyone else have any other methods?

Question

How would you determine whether two lines are parallel by looking at the equations of the lines in standard form.
I found a trick on one site saying that the slope of a standard equation (Ax + By = C) is equal to -A/B. Is this true? Does anyone else have any other methods?

amriju · Answer

look its not a trick..if u have two lines..bring them to the form y=mx+c..m and c being constants...if 'm' for both lines are equal..they are parellel...

anonymous · Answer

That I do understand. The problem is I need to be able to just look at two equations in standard form and determine if they are parallel or not, but other than the idea I stated, I'm not sure how to do so.

mokeira · Answer

It is true...its sort of a formula

anonymous · Answer

The -A/B?

anonymous · Answer

Is the -A/B the formula you're talking about? (just clarifying)

mokeira · Answer

if a line is $$y=mx+b$$
A line parallel to it will be
$$[y=mx+b]-1$$

anonymous · Answer

Okay...so would that mean that [Ax + By = C]-1 would be parallel to Ax + By = C?

mokeira · Answer

yes

mokeira · Answer

Plot and you will see

anonymous · Answer

Ah I see now. Thank you so much! :)

mokeira · Answer

Awesome! You're welcome

anonymous · Answer

Could I bother you another question about this?
Can you multiply the entire equation by -2, -3... instead of just -1 as well?

mokeira · Answer

if it is a plotted figure then the measurements will not be the same...it will be smaller but still parallel

mokeira · Answer

But just plot to confirm... Im not too sure