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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)?

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2 Answers

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!
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