6 7 Graphing Inequalities in Two Variables Today
6 -7 Graphing Inequalities in Two Variables Today you will need graph paper, a colored pencil, and a ruler. Algebra 1 Glencoe Mc. Graw-Hill Linda Stamper
Graphing A Linear Inequality The graph of a linear inequality in two variables is the graph of the solutions of the inequality. A boundary line divides the coordinate plane into two half-planes. The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions. y x
Graphing A Linear Inequality The graph of a linear inequality in two variables is the graph of the solutions of the inequality. A boundary line divides the coordinate plane into two halfplanes. The solution of a linear inequality in two variables is a half-plane. Shade the side of the half-plane that contains the solutions. y x
Graphing A Linear Inequality Use a dashed boundary line for < or >. A dashed line indicates that the points on the line are NOT solutions. Use a solid boundary line for < or >. A solid line indicates that the points on the line are solutions. y x
Graphing A Linear Inequality 1. Graph the corresponding equation, equation using a dashed line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form. 2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point. 3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Check whether the ordered pair (– 2, 3) is a solution of the (x, y) inequality. Write the inequality. Substitute values given in the ordered pair. Simplify. If statement is true, then the ordered pair is a solution. If statement is false, then the ordered pair is not a solution
Check whether the ordered pair is a solution of the inequality. Example 1 (0, 2) Example 2 (– 3, 5) Example 3 (0, 0) solution not a solution Which ordered pair was easiest to check?
Graphing A Linear Inequality 1. Graph the corresponding equation, equation using a dashed line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form. 2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point. 3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Check whether the ordered pair is a solution of the inequality. Example 1 (0, 2) Example 2 (– 3, 5) Example 3 (0, 0) solution not a solution Which ordered pair was easiest to check? Great to use as a test point because it’s easy to calculate!
Graphing A Linear Inequality 1. Graph the corresponding equation, equation using a dashed line (< or >) or a solid line ( < or >) to construct the boundary line. You may need to write the equation in slope-intercept form. 2. Test the coordinates of a point in one of the half-planes. You can use any point that is not on the line as a test point. 3. Shade the half-plane containing the test point if it is a solution of the inequality. If it is not a solution, shade the other half-plane.
Graph the inequality. Write the related equation (boundary line). Write in slope-intercept form. Graph the equation. Use a solid line. Test a point. Use (0, 0) if possible. Test is a solution, so shade half-plane that contains the test point. Use the inequality to test the point! • • • y solution x
x>2 Graph the inequality. Write the related equation. boundary line Graph the equation. Use a dashed line. Test a point. Use (0, 0) if possible. Test is false (not a solution), shade halfplane that does not contain the test point. Use the inequality to test the point! • y false not a solution x
Graph each inequality. Ex. 4 Ex. 5 Ex. 6 Ex. 7 Ex. 8 Ex. 9 Please copy all of the above problems in your spiral notebook!
Example 4 Graph the inequality. y y>– 3 boundary line • solution Use the inequality to test the point! x
Example 5 Graph the inequality. boundary line Use the inequality to test the point! y • • • solution x
Example 6 Graph the inequality. y • • boundary line not a solution • x
Example 7 Graph the inequality. y boundary line • • solution • x
Example 9 Example 8 • • x • • • y y x
6 -A 13 Pages 337– 339 # 8– 17, 27– 30, 33 -36, 48 -50.
- Slides: 19
