Determine whether the following pairs of lines are parallel, perpendicular, or neither.

y=2x+1 2x+y=7

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.