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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)

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Ron S. | Expert in Test Prep, Science, and MathExpert in Test Prep, Science, and Math
4.8 4.8 (51 lesson ratings) (51)
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...
slope here is 2 but slope of perpendicular line is 1/2
s0 y=mx+b 
y=mx+b so solve for b   b=4
soy=1/2x+4  A