How do you graph #3x - y < 4#?

1 Answer
Apr 10, 2015

First solve for y.

#3x-y<4# =

Subtract 3x from both sides.

#-y<-3x+4# =

Divide both sides by -1.

#-y/-1<-3x/-1+4/-1# =

#y>3x-4# (When dividing by a negative, the inequality symbol flips to its opposite.)

In order to graph this inequality, determine two points as if #y=3x-4#.

If #x=0#: #y=3*0-4=-4# Point A = #(0,-4)#

If #x=2#: #y=3*2-4=6-4=2# Point B = #(2,2)#

Graph those points, connecting them with a dashed line to denote that the graph is an inequality. Then shade in the area above the dashed line to show that y is greater than the points on the line.

graph{3x-y<4 [-15.79, 7.74, -6.36, 5.4]}