1. Unit 1.4 MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

2. Unit 1 – Algebra: Linear Systems, Matrices, & Vertex- Edge Graphs  1.4 – Graph Linear Inequalities in Two Variables  Georgia Performance Standard:  MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically. MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

3. Vocabulary  Linear inequality in two variables  Ax + By < C  Ax + By ≤ C  Ax + By > C  Ax + By ≥ C  Solution of a linear inequality  Ordered pair (x, y)  Graph of a linear inequality  Set of all points in a coordinate plane that represent solutions of inequality.  Half-planes  Divided by a line MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

4. How can we tell if a ordered pair is a solution of an inequality?  Substitute each ordered pair into the inequality  Does it make sense?  State your conclusion  ( _, _ ) is not a solution or…  ( _, _ ) is a solution MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

5. Graph Linear Inequalities  ≥ or ≤  When you graph an inequality that is greater than or equal to OR less than or equal the line you sketch (or draw) will be a solid line.  > or <  When you graph an inequality that is greater than or less than you will sketch (or draw) a dashed line. MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

6. Graph Linear Inequalities  You will have to shade your graph.  It is important to always look at the inequality and the number line. BOTH of these things will help you tell which way to shade the inequality! MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

7. Example:  Graph y ≥ 1 in a coordinate plane.

8. Example:  Graph 2x + y < -3

9. Solve a multi-step problem  The perimeter of a rectangle is to be more than 16 inches. Write an inequality describing the possible dimensions of the rectangle. Then graph the inequality and identify three solutions. MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

10. Graph an Absolute Value inequality  Things to know:  The number in front of the “| |” is the slope. If there is no number in front of it you can assume the slope is 1.  Whatever is inside the “| |” you do the opposite. This tells you which way to move the graph left or right.  If it is on the outside of the “| |” it tells you up or down. MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

11. Absolute Value y = |x+4| -3 MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.

12. Graph an absolute value inequality  Graph y ≤ |x| + 1

13. Homework  Page 19  1-4  7-9  10, 19-21  Page 21  5-7 MM3A6a – Solve systems of inequalities in two variables, showing the solutions graphically.