Which line is perpendicular to the line y = 1/2x + 2 ?

Question

Which line is perpendicular to the line y = 1/2x + 2 ?

Answer 1

The slope of ALL lines ⊥  to the line will be  -2/1

 

They will have the form y =  -2x + b, where b can be any real number.

Answer 2

Perpendicular lines have the property that their slopes are negative reciprocals of each other, that is 

 

m1 = -1 / m2  

 

The line y = (1/2)x + 2 has slope 1/2, so any line that has slope

 

m = -1 / (1/2) = -2 will be perpendicular to the given line 

 

So for example, 

 

y = -2x + 2

y = -2x - 2

y = -2x

 

are all perpendicular to y = (1/2)x + 2