Kristie Ferrentino

1. Find and graph the solution set of the inequality. 2. Determine the equation of a line that passes through the point (2,6) and has a slope of 5.

Students will be able to demonstrate their understanding of how to solve linear inequalities in two variables by graphing linear inequalities in two variables.

 Linear inequality graph: is a set of points in a coordinate plane that represent all of the possible solutions of that inequality  We represent the boundary line of the inequality by drawing the function represented in the inequality  Boundary Line: separates the coordinate plane into regions

InequalityType of LineShaded Region > (greater than)Above < (less than)Below ≥ (greater than and/or equal to)Above ≤ (less than and/or equal to)Below Dashed Line Solid Line

Less than Less than and/or equal to Greater than Greater than and/or equal to Inequality

Remember:  ≤ and ≥ will use a solid line  will use a dashed line Change the inequality sign to an equal sign; then graph the equation Step 1: Change the inequality sign, Graph the line

 Remember:  If greater than, greater than and/or equal to, shade above the inequality  If less than, less than and/or equal to, shade below the inequality  Can use a test point to check if the shaded part of the graph contains the inequality solutions. Step 2: Determine which half of the graph should be shaded

 Shade the part of the graph that contains the solutions. Step 3: Shade

 Step 1: Change the sign, and graph the line  Step 2: Determine which half of the graph should be shaded  Step 3: Shade Use a graph to solve y≤ 2x + 3

y ≤ 2x +3 Change the sign Test Point Test the point in original inequality True

Use a graph to solve y > -x + 4

Change sign Test Point Test the point in original inequality False y > -x + 4 Use a graph to solve y > -x + 4

Use a graph to solve the following inequalities 1. y < x y ≥ -3x y> x 4. y ≤ 2x - 4

1. What kind of line is less than or greater than? 2. What kind of line is greater than or equal to and less than or equal to? 3. If the inequality is greater than, greater than or equal to, what part of the graph is shade? 4. If the inequality is less than, less than or equal to, what part of the graph is shade? 5. What are the three steps to graphing linear inequalities?