Strategy: Figure out what the line would look like using #2y-3x=6#. Then, plugging in a few choice points, find #x# and #y# values that, when plugged in, are truly greater than #6#. Shade the side where the inequality is true.
Step 1. Graph the line #2y-3x=6#
Rewrite this equation with #y# on one side alone.
#2y=3x+6#
#y=3/2x+3#
Slope: #m=3/2#, that is a rise of 3 and run of 2
#y#-intercept: #(0, 3)#
graph{y=3/2x+3}
Step 2. Find some points where #x# and #y# will make the inequality true.
Try the point #(0,0)#:
#2(0)-3(0)>6# or #0>6# is FALSE. Do not shade this side of the line.
Try the point #(-5,0)#:
#2(0)-3(-5)>6# or #15>6# is TRUE. So, do shade this side of the line.
Because the inequality is #>#, use a dashed line.
graph{2y-3x>6}
