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 $P_1$

$3=9/4xx2+c$

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

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