parallel, perpendicular, or neither

Question

1. y-4=-3(x+5)

y+3=-1/3(x+1)

1. y=-1/2x-4

y+2=-1/2(x-7)

Answer 1

First rearrange the equations into slope-intercept form:

y = mx + b

where m is the slope and b is the y-intercept.

Once in that form you can easily compare the slopes. As Paul M. states previously, the equations are parallel when they have the same slope.

So for the first equation:

y - 4 = 3(x + 5)

y - 4 = 3x + 15 (distribute the 3)

y = 3x + 19 (isolate y on left side of equation to get slope-intercept form y = mx + b)

Here you can see the slope is 3.

Rearrange the other 3 equations into the slope-intercept form, and you will see why Paul M. is correct.

Answer 2

parallel: the slopes are the same

perpendicular: the slopes are the "negative inverse"---eg if the slope of a function is +2. then the perpendicular line has a slope of -1/2

Answer 3

The last lines represented by the last 2 equations are parallel...because the equations have the same slope.