Question 146775

{{{3x+4y>=12}}} Start with the given inequality.



{{{3x+4y=12}}} Replace the inequality sign with an equals sign.



{{{4y=12-3x}}} Subtract {{{3x}}} from both sides.



{{{y=(12-3x)/(4)}}} Divide both sides by {{{4}}} to isolate {{{y}}}.



{{{y=-(3/4)x+3}}} Rearrange the terms.



So in order to plot {{{3x+4y>=12}}} or {{{y>=-(3/4)x+3}}} (which is the same thing), we need to plot the equation {{{y=-(3/4)x+3}}} 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,-(3/4)x+3) }}} Graph of {{{y=-(3/4)x+3}}}



Now plug in a test point (0,0) into the inequality {{{y>=-(3/4)x+3}}}



{{{y>=-(3/4)x+3}}} Start with the given inequality.



{{{0>=-(3/4)*(0)+3}}} Plug in {{{x=0}}} and {{{y=0}}}



{{{0>=3}}} Evaluate and simplify.



Since the inequality is false, this means that we shade the entire region that does <b>NOT</b> contain the point (0,0)



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



 {{{drawing( 500, 500, -10, 10, -10, 10,
    graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+0),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+1.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+3),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+4.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+6),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+7.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+9),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+10.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+12),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+13.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+15),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+16.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+18),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+19.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+21),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+22.5),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3+24)

 )}}} Graph of {{{y>=-(3/4)x+3}}} with the shaded region in green