Answer
Refer to the graph below.
Work Step by Step
Divide both sides of the equation by $144$ to obtain:
$\dfrac{16x^2+9y^2}{144}=\dfrac{144}{144}
\\\dfrac{x^2}{9}+\dfrac{y^2}{16}=1
\\\dfrac{x^2}{3^2}+\dfrac{y^2}{4^2}=1$
This means that the given equation is equivalent to the equation above.
Recall:
The graph of the equation $\dfrac{x^2}{b^2}+\dfrac{y^2}{a^2}=1$ where $a\gt b$ is a vertical ellipse whose center is at $(0, 0)$ and whose major axis is $2a$ units long and whose minor axis is $2b$ units long.
The equation above is in the same form as the one in the recall part above with $a=4$ and $b=3$.
Thus, its graph is an ellipse whose center is at $(0, 0)$. with a major axis at is 8 units long and a minor axis that is 6 units long.
To graph the given equation, perform the following steps:
(1) Plot the following points:
center: $(0, 0)$
vertices: $(0, 4)$ and $(0, -4)$ (the endpoints of the major axis)
endpoints of the minor axis: $(-3 ,0)$ and $(3, 0)$
(2) Connect the points (excluding the center) using a smooth curve to form an ellipse.
Refer to the graph in the answer part above.
