Question 146903


{{{5x+6y<=30}}} Start with the given inequality.



{{{5x+6y=30}}} Replace the inequality sign with an equals sign.



{{{6y=30-5x}}} Subtract {{{5x}}} from both sides.



{{{y=(30-5x)/(6)}}} Divide both sides by {{{6}}} to isolate {{{y}}}.



{{{y=-(5/6)x+5}}} Rearrange the terms.



So in order to plot {{{5x+6y<=30}}} or {{{y<=-(5/6)x+5}}} (which is the same thing), we need to plot the equation {{{y=-(5/6)x+5}}} 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,-(5/6)x+5) }}} Graph of {{{y=-(5/6)x+5}}}



Now plug in a test point (0,0) into the inequality {{{y<=-(5/6)x+5}}}



{{{y<=-(5/6)x+5}}} Start with the given inequality.



{{{0<=-(5/6)*(0)+5}}} Plug in {{{x=0}}} and {{{y=0}}}



{{{0<=5}}} 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, -10, 10, -10, 10,
    graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-0),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-1.66666666666667),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-3.33333333333333),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-5),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-6.66666666666667),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-8.33333333333333),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-10),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-11.6666666666667),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-13.3333333333333),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-15),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-16.6666666666667),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-18.3333333333333),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-20),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-21.6666666666667),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-23.3333333333333),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-25),
graph( 500, 500, -10, 10, -10, 10,-(5/6)x+5,-(5/6)x+5-26.6666666666667)

 )}}} Graph of {{{y<=-(5/6)x+5}}} with the shaded region in green