we know that if f(a)=b then [tex]f^{-1}(b)=a[/tex]
and
if [tex]f^{-1}(a)=b[/tex] then f(b)=a
so
since [tex]f^{-1}(0)=-2[/tex] therefor, f(-2)=0
we have 2 points, (-2,0) and (0,3)
we can use slope intercept form
y=mx+b
m=slope
b=y intercept
we have when x=0, y=3, that is the y intercept
y=mx+3
substitute the other point
(-2,0)
x=-2, y=0
0=-2m+3
-3=-2m
divide both sides by -2
[tex]\frac{3}{2}=m[/tex]
the equation is
[tex]y=\frac{3}{2}x+3[/tex]
or
3x-2y=-6 in standard form
