<image>In the rectangular Cartesian coordinate system, the graph of the linear function $$y=ax+b(a \neq 0)$$ intersects with the graph of the inverse proportional function $$y= \dfrac {k}{x}(k \neq 0)$$ at points $$A$$ and $$B$$ in the second and fourth quadrants, respectively, and intersects the $$y$$-axis at point $$C$$. From point $$A$$, draw $$AH \perp y$$-axis with the foot of the perpendicular as $$H$$, and $$OH=3$$, $$\tan ∠AOH= \dfrac {4}{3}$$. The coordinates of point $$B$$ are $$(m,-2)$$.
$$(1)$$ Calculate the perimeter of $$\triangle AHO$$; 
$$(2)$$ Find the equations of the given inverse proportional function and linear function.