Answer: f(x) = 3x+12
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Work Shown:
f(x) = (-1/3)x+8 is the same as y = (-1/3)x+8
Compare this to y = mx+b. The slope is m = -1/3
Flip the fraction to get -1/3 turn into -3/1 = -3. Then flip the negative to positive getting m = 3 as the perpendicular slope.
Side note: the original slope and perpendicular slope multiply to -1.
We want this new equation to go through (x,y) = (-2,6) due to the notation f(-2) = 6
So,
y = mx+b
y = 3x+b ... plug in the perpendicular slope
6 = 3(-2)+b ... plug in the given point's coordinates
6 = -6+b
6+6 = b ... add 6 to both sides
12 = b
b = 12
Therefore the equation y = mx+b becomes y = 3x+12 which is equivalent to f(x) = 3x+12