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

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)

### 2 Answers by Expert Tutors

Ron S. | Expert in Test Prep, Science, and MathExpert in Test Prep, Science, and Math
4.8 4.8 (51 lesson ratings) (51)
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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!
OLUWASEUN O. | Tutor in Math, Pre-Medical/Medical courses and Fitness/Martial Arts,Tutor in Math, Pre-Medical/Medical cours...
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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