Question 146526


{{{x/5+y/4<1}}} Start with the given inequality.



{{{x/5+y/4=1}}} Replace the inequality sign with an equals sign.



{{{20(x/5+y/4)=20(1)}}} Multiply both sides by the LCD {{{20}}} to clear any fractions.



{{{4x+5y=20}}} Distribute and multiply.



{{{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.



So in order to plot {{{x/5+y/4<1}}} or {{{y<-(4/5)x+4}}} (which is the same thing), we need to plot the equation {{{y=-(4/5)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,-(4/5)x+4) }}} Graph of {{{y=-(4/5)x+4}}}



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



{{{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, -10, 10, -10, 10,
    graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-0),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-1.6),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-3.2),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-4.8),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-6.4),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-8),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-9.6),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-11.2),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-12.8),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-14.4),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-16),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-17.6),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-19.2),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-20.8),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-22.4),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-24),
graph( 500, 500, -10, 10, -10, 10,-(4/5)x+4,-(4/5)x+4-25.6)

 )}}} Graph of {{{y<-(4/5)x+4}}} with the shaded region in green