Question 146412
{{{4x+5y<=20}}} Start with the given inequality.



{{{4x+5y=20}}} Replace the inequality sign with an equals sign.



{{{5y=20-4x}}} Subtract {{{4x}}} from both sides.



{{{y=(20-4x)/(5)}}} Divide both sides by {{{5}}} to isolate {{{y}}}.





{{{y=-(4/5)x+4}}} Rearrange the terms and simplify.



So in order to plot {{{4x+5y<=20}}} or {{{y<=-(4/5)x+4}}} (which is the same thing), we need to plot the equation {{{y=-(4/5)x+20}}} first. 
(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,-(4/5)x+4) }}} Graph of {{{y=-(4/5)x+4}}}



Now plug in a test point (0,0) into the inequality {{{y<=-(4/5)x+20}}}



{{{y<=-(4/5)x+4}}} Start with the given inequality.



{{{0<=-(4/5)*(0)+4}}} Plug in {{{x=0}}} and {{{y=0}}}



{{{0<=4}}} Evaluate and simplify.



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



In other words, we simply shade the <b>entire</b> region that is below the line.


{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-3),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-6),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-9),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-12),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-15),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-18),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-21),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-24),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-27),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-30),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-33),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-36),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-39),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-42),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-45),
graph( 500, 500, -20, 20, -20, 20,-(4/5)x+4,-(4/5)x+4+-48))}}} Graph of {{{y<=-(4/5)x+4}}} with the shaded region in green