Graphing Linear Inequalities in Two Variables graph a linear inequality in two variables model a real life situation with a linear inequality.

Recall… Graph n < 3 on a number line. -3 -2 -1 0 1 2 3 4

Graphing an Inequality in Two Variables Graph x < 2 Step 1: Start by graphing the line x = 2 Now what points would give you less than 2? Since it has to be x < 2 we shade everything to the left of the line.

Graph x -2 on the coordinate plane. y x

Graph y > 3 on the coordinate plane. x

Graphing a Linear Inequality Sketch a graph of y  3

Some Helpful Hints If the sign is > or < the line is dashed If the sign is  or  the line will be solid When dealing with just x and y. If the sign > or  the shading either goes up or to the right If the sign is < or  the shading either goes down or to the left

Step 1: Put into slope intercept form Using What We Know Sketch a graph of x + y < 3 Step 1: Put into slope intercept form y <-x + 3 Step 2: Graph the line y = -x + 3

When dealing with slanted lines If it is > or  then you shade above If it is < or  then you shade below the line

> < Graph y -3x + 2 on the coordinate plane. y Instead of testing a point If in y = mx + b form... Shade up Shade down Solid line x > < Dashed line

-3x -3x -4y > -3x + 12 -4 -4 Graph on the coordinate plane. -4 -4 y < x - 3 x Boundary Line m = b = -3

Graph y -3x + 2 on the coordinate plane. Boundary Line y = -3x + 2 m = -3 b = 2 x Test a point not on the line test (0,0) 0 -3(0) + 2 Not true!

Problem If you have less than $5.00 in nickels and dimes, find an inequality and sketch a graph to describe how many of each coin you have. Let n = # of nickels Let d = # of dimes 0.05 n + 0.10 d < 5.00 or 5 n + 10 d < 500

5n + 10d < 500 n d d 50 60 50 40 30 20 10 100 n 0 10 20 30 40 50 60 70 80 90 100

Graphing Absolute Value Inequalities

Graphing Absolute Value Inequalities