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The general equation for a line is y=ax+b, right? If two lines are to never coincide, they have to be parallelle, stretching both ways to infinity wihtout meeting.

So if you put both your equations on the general form, getting this:

y1=ax+b

y2=cx+d

The only way these lines are parallelle is if a=c. So whenever a differs from c, your line will coincide at some point. (to find this point, set y1 = y2 and solve the equation for x, giving you the x-value for their point of coincision).

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Q: How do you know if two lines are coinciding based on their equations?
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