First, put the inequality into slope-intercept form:
9x-2y<=-189x−2y≤−18
-2y<=-18-9x−2y≤−18−9x
2y>=18+9x2y≥18+9x
2y>=9x+182y≥9x+18
y>=9/2x+9y≥92x+9
Now, graph the line y=9/2x+9y=92x+9. Since the inequality has "or equal to" in it, you can make this line solid (as opposed to dashed). The next step is to figure which side of the line to shade.
A strategy that is effective for me is to plug in the point (0,0)(0,0), the origin, into the function and see if it stays true. If it does, then the region containing that point is shaded, and the other region isn't. Otherwise, the region that doesn't contain the point (0,0)(0,0) is shaded.
Plugging in (0,0)(0,0):
y>=9/2x+9=>y≥92x+9⇒
0>=9/2(0)+90≥92(0)+9
0>=0+90≥0+9
0>=90≥9
Since this is false, that means you have to shade the region not containing the origin. Here's what the graph looks like:
graph{y>=9/2x+9 [-10, 10, -5, 5]}
