Question 145959


{{{3x+4y<12}}} Start with the 1st inequality



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



{{{y=-(3/4)x+3}}} Solve for y



So in order to plot {{{y<-(3/4)x+3}}}, we need to plot the equation {{{y=-(3/4)x+3}}} first



{{{ 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}}}



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



{{{0<3}}} Evaluate and simplify



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



 {{{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+3-2),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-4),
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+3-8),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-10),
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+3-14),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-16),
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+3-20),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-22),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-24),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-26),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-28),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-30),
graph( 500, 500, -10, 10, -10, 10,-(3/4)x+3,-(3/4)x+3-32)

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