Linear inequalities You know how to graph expressions like these:

Today we’ll expand that to expressions like …. y < 3x – 1 Today we’ll expand that to expressions like … y < 3x – 1 If you can graph a line, you can graph an inequality.

To graph: •. Find the associated line. (think what it would be if it To graph: • Find the associated line (think what it would be if it said = instead of < or >)

•. If < or >, graph a dotted. line • • If < or >, graph a dotted line • If < or >, graph a solid line.

• If < or <, shade below the line.

• Of > or >, shade above the line.

Graph y < 2x - 4

Graph y < 2x - 4

Graph y < -x + 1

Graph y < -x + 1

Graph y > -½ x – 3

Graph y > -½ x – 3

What inequalities are graphed?

What inequalities are graphed? y < -2/3x + 6

y > x + 1

If the line is not in slope/intercept form, you can tell which side to shade by picking a point on one side and seeing if it works in the expression.

For example … x + 2y < 8 . You could graph with the For example … x + 2y < 8  You could graph with the intercepts (8,0) and (0,4).  It will be a dotted line.

x + 2y < 8 Pick a point not on the line (like (0,0) … the easiest point possible). 0 + 20 < 8 Since this works, we shade in the direction of (0,0).

x + 2y < 8 Here’s the final answer:

x + 2y < 8 If you had picked a point on the other side of the line (like (4,4), for instance) … 4 + 24 is NOT < 8 So you’d shade the other way.