Question

Determine whether the following pairs of lines are parallel,perpendicular,or neither.
y=2x+1 2x+y=7

Answer 1

In order to answer this one, you have to remember:

--> Parallel lines have equal slopes.

--> Perpendicular lines have negative reciprocal slopes.

                       (One slope  =  - [ 1/the other slope ]

The question gives us two lines:

#1).  y = 2x + 1
#2).  2x + y = 7

The first equation is in nice slope-intercept form, and we can see
right away that the slope of its graph is  2 .

The second equation is not in slope-intercept form, so we need to
massage it slightly before we can spot the slope of its graph.

                                            2x + y =          7

Subtract  2x  from each side:      y = -2x + 7 .  <== slope-intercept form.
                                                                                Slope = -2 .
Now we know both slopes.

#1).  Slope =  2
#2).  Slope = -2

Are the slopes equal ?  I don't think so.  2  is not equal to  -2 .
The lines are not parallel. 

Are the slopes negative reciprocals ?  I don't think so. 
2 is not equal to  -[ 1/(-2) ].
The lines are not perpendicular.