power!!!!!?

Question by Eleanor C: power!!!!!?
write a power function passing through the points

(5, 12) (7, 25)

hmm. i made a system and i solved for a and plugged in a, but then i got stuck…
power function is y=ax^b

Best answer:

Answer by Math Tutor
First find the slope:

Slope = m = ∆y/∆x = (25-12)/(7-5) = 13/2

Now use any given point to find b:

y = mx + b
12 = (13/2)(5) + b
12 = 65/2 + b
b = 12 – 65/2
b = (24-65)/2
b = -41/2

Then f(x) = (13/2)x – 41/2

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