How do you determine if these are Perp., Parrell, or niether??

Question

I do not want the answer, just HOW to do this.

1. y+5=-x

x-y=2

2. 3x-5y=7y

7y-3x=7

Answer 1

I think that you need to put them in y=mx + b format.  If you do, m represents the slope of the line.  You may graph them to find out from there.

1. y+5=-x        or   y = -x - 5    (-1 is the slope, because it's -1 x)

x-y=2              or   y = x + 2    (1 is the slope, because it's +1 x)

I'd graph these to see if they're perpendicular, but since the first slope is negative (the line angles down from left to right) and the second slope is positive (the line angles up from left to right), then I'd guess they're not parallel.  -5 is where the first line crosses the y-axis and +2 is where the second line crosses the y-axis.

2. 3x-5y=7y    or y = 1/4 x + 0

7y-3x=7         or y = 3/7 x + 1

I'd graph these to see if they're parallel or perpendicular.  0 is where the first line crosses the y-axis and +1 is where the second line crosses the y-axis.

Hope that helps.

Answer 2

Perpendicular lines have opposite slopes.

1st line has slope x/y

2nd perpendicular line has slope -y/x

Parallel lines have same slopes.

1st line has slope x/y

2nd line has slope x/y