Answer
Please see the graph.
Work Step by Step
Green line: $3x+y<9$
$3x+y-3x<9-3x$
$y < 9-3x$
Since we have the "less than" sign, we use a dotted line. Let's use the point $(0,0)$ to see what side of the line we shade.
$y < 9-3x$
$0 < 9-3*0$
$0 < 9-0$
$0 < 9$ (true)
Since this is true, we shade the side of the line that has the point $(0,0)$.
Red line: $y\le2$
Since we have the "less than or equal to" sign, we use a solid line. Let's use the point $(0,0)$ to see what side of the line we shade.
$y\le2$
$0 \le 2$ (true)
Since this is true, we shade the side of the line that has the point $(0,0)$.
The union of the two lines is the area that is shaded red or green.