Answer
The plane is parallel to the $z$-axis. The trace is the line $x+2y=6$.
![](https://gradesaver.s3.amazonaws.com/uploads/solution/23dc23f7-8ef4-41a9-8d2c-e7c7bbf1f82a/result_image/1602629529.gif?X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAJVAXHCSURVZEX5QQ%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T004014Z&X-Amz-Expires=900&X-Amz-SignedHeaders=host&X-Amz-Signature=22267f69e43742a6cc6eba3a16cf4af10f1071a66e451e5148778c3624c99a0b)
Work Step by Step
To draw the plane, we determine its intersections with the coordinate axes. Since $z$ coordinate is not present in the equation, it does not intersects the $z$-axis. So, the plane is parallel to the $z$-axis.
To find where it intersects the $x$-axis, we set $y=0$ and obtain $x=6$.
It intersects the $y$-axis when $x=0$. So, $y=3$.
Thus, the trace is the line $x+2y=6$. The plane is shown in the figure attached.