i'm from Michigan originally :). Anyway, here is how you graph an inequality:
1. Put the function into slope-intercept form:
-5x - 2y <= -8
-2y <= 5x - 8
y >= -(5/2)x + 4 (you flip the inequality symbol when you divide both sides by a negative)
2. Look at whether the inequality is less than or greater than; if it is, then you use a dotted line. But, if it is either less than or equal to or greater than or equal to, you use a solid line.
3. Graph the function as if it were a typical function (in this case, graph y = (-5/2)x + 4
4. Then shade either below or above the line. Since this is y>= (-5/2)x + 4, you shade above the function line. If it were less than, you would shade below.