Question 146656


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



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



{{{3y=12+4x}}} Add {{{4x}}} to both sides.



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



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



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



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



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



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



{{{0>4}}} 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,(4/3)x+4),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+0),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+2.66666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+5.33333333333333),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+8),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+10.6666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+13.3333333333333),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+16),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+18.6666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+21.3333333333333),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+24),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+26.6666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+29.3333333333333),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+32),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+34.6666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+37.3333333333333),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+40),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+42.6666666666667),
graph( 500, 500, -10, 10, -10, 10,(4/3)x+4,(4/3)x+4+45.3333333333333)

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