What is the equation of a line that is perpendicular to y=2x+4 and passes through the point (4,6)?

Question

A. y=1/2x+4

B. y=-1/2x+4

C. y=-1/2x+6

D. y=-1/2x+8

 

(I feel it's between A or B)

Answer 1

Actually the slope of the perpendicular would be -1/2, giving you

 

y = (-1/2)x + b through the point (4,6)

 

substituting, we get 6 = (-1/2)4 + b, which simplifies to 6 = -2 + b, or 8 = b

 

The final equation would be y = (-1/2)x + 8, which is answer D.

 

Another way to approach this is to plug the number 4 into each of the answer choices, and see which equation yields 6 for y:

 

A gives you 6

B gives you 2

C gives you 4

D gives you 6

 

So you can eliminate B&C, and since a perpendicular is the negative inverse of the original it has to be D

 

Hope this helps!

Answer 2

slope here is 2 but slope of perpendicular line is 1/2

s0 y=mx+b 

y=6

x=4

m=1/2    

 

y=mx+b so solve for b   b=4

 

soy=1/2x+4  A