# How do you graph the inequality 3x+4y

Graph the line of ##(3x+4y=12)## using two arbitrary solutions;
then shade in the side of the line containing the point ##(0,0)##

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##3x+4y<=12##
includes all points on the line ##3x+4y=12##

The x and y intercepts provide a convenient pair of points on this line (although any other pairs would work).
##color(white)(“XXX”)x=0 rarr y=4##
##color(white)(“XXX”)y=0 rarr x=3##
so the pairs ##(0,4)## and ##(3,0)## are on this line.
Plot these point and draw a line through them.

Since the inequality is true for ##(x,y)=(0,0)##
the point ##(0,0)## must be on the selected side of the line just drawn.
graph{3x+4y <= 12 [-10, 10, -5, 5]}

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