jmc

To approach this problem, we can either use long division or synthetic division to evaluate the quotient of the given rational expression. Alternatively, we can rewrite the numerator as $2x^2+3x-7$ $=2x^2+3x-7-9x+9x$ $=2x(x-3)+9x-7-20+20$ $=2x(x-3)+9(x-3)+20$. Hence, $$y=\frac{2x^2+3x-7}{x-3}=\frac{(2x+9)(x-3)+20}{x-3}=2x+9+\frac{20}{x-3}.$$As $x$ approaches infinity or negative infinity, then the fraction approaches $0$, and $y$ approaches $2x+9$.Thus, $m+b=\boxed{11}.$