Question 102228
First graph the line {{{y=x-2}}} (just replace the inequality sign with an equal sign) (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)



{{{ graph( 500, 500, -10, 10, -10, 10, x-2) }}}




Now lets pick a test point, say (0,0). Any point will work, (just make sure the point doesn't lie on the line) but this point is the easiest to work with. Now evaluate the inequality {{{y>=x-2}}} with the test point


Substitute (0,0) into the inequality

{{{(0)>=(0)-2}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0>=-2}}} Simplify



Since this inequality is true, we simply shade the entire region that contains (0,0)

{{{drawing( 500, 500, -20, 20, -20, 20,
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+1.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+3),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+4.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+6),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+7.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+9),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+10.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+12),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+13.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+15),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+16.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+18),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+19.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+21),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+22.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+24),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+25.5),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+27),
graph(  500, 500, -20, 20, -20, 20,x-2,x-2+28.5))}}} Graph of {{{y>=x-2}}} with the boundary (which is the line {{{y=x-2}}} in red) and the shaded region (in green)