How do you write a power model for the function that passes through the points ( 2, 3) and (6, 12)?

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Answer 1 · 2017-12-17T22:06:39

Assuming this is a straight line

#y=4/9x-3/2#

Using the standard form #y=mx+c# where #m# is the gradient

#m=("change in y")/("change in x") color(white)("d")# reading left to right on the x-axis

Set the left most point as #P_1->(x_1,y_1) = (2,3)#
Set the right most point as #P_2->(x_2,y_2)=(6,12)#

#m=("change in y")/("change in x") ->(y_2-y_1)/(x_2-x_1) = (12-3)/(6-2) = 9/4#

As #m>0# then the gradient (slope) is upwards reading left to right
It goes up 9 for every 4 along.

To determine the value of #c# substitute a known point. I choose #P_1#

#3=9/4xx2+c#

#c=3-9/2color(white)("ddd") ->color(white)("ddd") 6/2-9/2color(white)("d")= color(white)("d")-3/2#

#y=4/9x-3/2#