Question

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

Answer 1

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]}