Math CentralQuandaries & Queries


Question from Conor, a student:


I was wondering if you could help me with this question :)


are these lines parallel?

y = 3x -2 and 6y = 3x +2

Hi Conor.

Parallel lines have the same slope. If you turn both equations into the y = mx+b form (the first equation is already in this form) then you can compare the "m" values. If they are the same, and the sign (pos/neg) is the same and the values of "b" are different, then the lines are parallel.

Example: Are these lines parallel? y = 0.6x - 4 and 8 = 3x - 5y
Solution: first change the second equation into y = mx + b form:

8 = 3x - 5y
5y = 3x - 8
y = (3/5)x - (8/5)
m = 3/5 = 0.6

This is the same as the m in the first equation, so yes, these two lines are parallel.

You try yours using the same idea.

Hope this helps,
Stephen La Rocque

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