Answer
The error is in writing point-slope form of the equation as $y-y_{1}=mx-x_{1}$ instead of $y-y_{1}= m(x-x_{1})$.
The corrected linear function is $g(x)=-3x+19$.
Work Step by Step
Using the correct point-slope form of the equation, We have
$y-4=-3(x-5)$
$\implies y-4=-3x+15$
$\implies y=-3x+15+4$
$\implies y=-3x+19$
$\implies g(x)=-3x+19$
