How do you graph #3x+y<5#?
1 Answer

The first step is to treat the inequality as an equality.
#3x + y = 5# 
Then find coordinates that will create the border of the area that is represented by the inequality.
(I usually rewrite the equation into slopeintercept form
#y = 3x + 5# and graph that.) 
Instead of graphing a straight line use a dotted line, since the original inequality
#3x + y < 5# is less than rather then less than or equal.
graph{3x + y < 5 [10, 10, 5, 5]} 
To decide which side of the line to graph, pick a coordinate pair on either side of dotted line. (I usually use
#(0, 0)# ) and see if it makes the inequality true.
ex. Is#(0, 0) # part of the solution set ?
#3x + y < 5#
#3(0) +0 < 5#
#0 < 5 # is a true statement so the left side of the dotted line should be shaded