How do you graph the inequality #3x-y<=6 #?

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Answer 1 · 2017-05-26T02:43:14

See the explanation.

Graph:

#3x-y>=6#

Change the equation to the slope intercept form by solving for #y#.

Subtract #3x# from both sides.

#color(red)cancel(color(black)(3x))-color(red)cancel(color(black)(3x))-y>=6-3x#

Simplify.

#-y>=-3x+6#

Multiply both sides by #-1#. This will change the direction of the inequality.

#y<=3x-6#

Determine some points on the line by picking values for #x# and solving for #y#.

Points
#x=-2,##y=-12#
#x=0,##y=-6#
#x=2,##y=0#

Plot the points, and draw a straight solid line through them. Then shade the area below the line.

Graph graph{y<=3x-6 [-15.7, 16.32, -13.07, 2.95]}