ANSWER
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]
EXPLANATION
The given non-linear function is a hyperbola with equation:
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} = 1[/tex]
Since the boundary lines are dashed lines, the inequality should be either < or >.
Since the outer portion is shaded, the inequality is
[tex] \frac{( {x + 3)}^{2} }{16} - \frac{( {y + 4)}^{2} }{36} > 1[/tex]
