Determine whether each pair of lines is parallel, perpendicular, or neither

Question

2x=y+7 and y=2x+3

 

Answer 1

First, put these lines into slope-intercept form (y = mx + b):

 

2x = y + 7

2x - 7 = y

y = 2x - 7

 

y = 2x + 3

 

Now, compare the lines' slopes (m-values). 2 = 2, so either the lines are parallel or they are the same line.

 

Compare the lines' y-intercepts (b-values). -7 ≠ 3, so the lines are not the same. That means the lines are parallel.