Answer
Please see the graph.
Work Step by Step
$x^2 – y^2/9 \le 1$
We pick the points $(-2,0)$, $(0,0)$, and $(2,0)$ to determine what side of the line to shade.
$(-2,0)$
$x^2 – y^2/9 \le 1$
$(-2)^2 – 0^2/9 \le 1$
$4- 0/9 \le 1$
$4 -0 \le 1$
$4 \le 1$ (false)
$(0,0)$
$x^2 – y^2/9 \le 1$
$0^2 – 0^2/9 \le 1$
$0 – 0/9 \le 1$
$0 -0 \le 1$
$0 \le 1$ (true, so we shade the side of the line with this point)
$(2,0)$
$x^2 – y^2/9 \le 1$
$(2)^2 – 0^2/9 \le 1$
$4- 0/9 \le 1$
$4 -0 \le 1$
$4 \le 1$ (false)
