How do you graph the inequality #3x+4y<=12#?

1 Answer
Alan P.
Oct 15, 2015

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

Explanation:

#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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