```Question 112885
In order to graph {{{2x+y<=-5}}}, we need to graph the <b>equation</b> {{{2x+y=-5}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{2x+y=-5}}} (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, -20, 20, -20, 20, -2x-5) }}} graph of {{{2x+y=-5}}}

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 {{{2x+y<=-5}}} with the test point

Substitute (0,0) into the inequality

{{{2(0)+(0)<=-5}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0<=-5}}} Simplify

(note: for some reason, some of the following images do not display correctly in Internet Explorer. So I recommend the use of <a href=http://www.mozilla.com/en-US/firefox/>Firefox</a> to see these images.)

Since this inequality is <font size=4><b>not</b></font> true, we do <font size=4><b>not</b></font> shade the entire region that contains (0,0). So this means we shade the region that is on the opposite side of the line

{{{drawing( 500, 500, -20, 20, -20, 20,
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-3),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-6),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-9),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-12),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-15),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-18),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-21),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-24),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-27),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-30),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-33),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-36),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-39),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-42),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-45),
graph(  500, 500, -20, 20, -20, 20,-2x-5,-2x-5+-48))}}} Graph of {{{2x+y<=-5}}} with the boundary (which is the line {{{2x+y=-5}}} in red) and the shaded region (in green)

```