I can graph linear inequalities in two variables and use linear inequalities when modeling real- world situations. 6.5 LINEAR INEQUALITIES

 A linear inequality in two variables (ex: y > x – 3) can be formed by replacing the equal sign with an inequality symbol.  A solution of an inequality is an ordered pair (x,y) that makes the inequality true. SOLUTION OF A LINEAR INEQUALITY

 Is the ordered pair a solution to the inequality y > x – 3?  (1,2)  Substitute values for x and y: 2 > 1 – 3  Simplify: 2 > -2  Check if this is true: yes! It is a solution.  (-3,-7)  No! This is not a solution. PRACTICE

 It should still be in slope-intercept form  So we still use a slope and y-intercept to graph.  Use a dashed line if > or < but not equal to  Use a solid line if ≤ or ≥  If y is greater than, shade above the line  If y is less than, shade below the line. GRAPHING A LINEAR INEQUALITY

 What is the graph of y > x – 2?  Graph y = x – 2  Use a dashed line  Shade above the line since it is greater than YOU TRY!

 What is the graph of x > -1?  Graph x = -1  Use a dashed line  Shade to the right since x is greater than GRAPHING IN ONE VARIABLE

 What is the graph of y ≥ 2? YOU TRY!

 An interior decorator will remodel the kitchen as shown and can only spend $420 or less. What are 3 possible prices for wallpaper and tile?  Write an inequality  24x + 12y ≤ 420  Write in slope-int form  y ≤ -2x +35  Graph and pick 3 solutions.  $5 and $5  $10 and $10  $5 and $20 MODELING WITH INEQUALITIES

 Odds p.397 #9-37 ASSIGNMENT