```Question 87377
In order to graph {{{4x+y>4}}}, we need to graph the <b>equation</b> {{{4x+y=4}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{4x+y=4}}} (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, -4x+4) }}} graph of {{{4x+y=4}}}

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{4x+y>4}}}

Substitute (0,0) into the inequality

{{{4(0)+(0)>4}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0>4}}} Simplify

Since this inequality is <b>not</b> true, we do <b>not</b> 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,-4x+4,-4x+4+5),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+10),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+15),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+20),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+25),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+30),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+35),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+40),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+45),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+50),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+55),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+60),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+65),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+70),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+75),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+80),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+85),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+90),
graph(  500, 500, -20, 20, -20, 20,-4x+4,-4x+4+95))}}} Graph of {{{4x+y>4}}} with the boundary (which is the line {{{4x+y=4}}} in red) and the shaded region (in green)
(note: since the inequality contains a greater-than sign, this means the boundary is excluded. This means the solid red line is really a dashed line)
```