Question 581035: Find the equation of the rational function with horizontal asymptote y=-6 and that passes through the points (-2,-2) and (1,-5). I know you have to plug in the points for x and y, and I know how to solve questions already giving you 2 asymptotes, but I'm completely lost on this. o.o
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Find the equation of the rational function with horizontal asymptote y=-6 and that passes through the points (-2,-2) and (1,-5). I know you have to plug in the points for x and y,
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y = (6x+a)/(x+b)
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Substitute each point to be 2 equations in a and b.
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-2 = (-12+a)/(-2+b)
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-5 = (6+a)/(1+b)
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Rearrange each equation:
4-2b = -12+a
-5-5b = 6+a
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Rearrange:
a + 2b = 16
a + 5b = -11
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Subtract and solve for "b":
3b = -27
b = -9
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Solve for "a":
a + 2b = 16
a + 2*-9 = 16
a -18 = 16
a = 34
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Equation:
y = (6x - 34)/(x-9)
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Cheers,
Stan H.
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