Presentation on theme: "6. 5 Graphing Linear Inequalities in Two Variables 7"— Presentation transcript:
1 6. 5 Graphing Linear Inequalities in Two Variables 7 6.5 Graphing Linear Inequalities in Two Variables 7.6 Graphing Linear Inequalities SystemObjectives1. Graph linear inequalities.2. Graph systems of linear inequalities.
2 Linear InequalitiesA linear inequality in two variables is an inequality that can be written in the formAx + By < C,where A, B, and C are real numbers and A and B are not both zero. The symbol < may be replaced with , >, or .The solution set of an inequality is the set of all ordered pairs that make it true. The graph of an inequality represents its solution set.
3 To Graph a Linear Inequality Step(1) Solve for y, convert the inequalities to Slope-Intercept Form. If one variable is missing, solve it and go to step (2).(2) Graph the related equation.** If the inequality symbol is < or >, draw the line dashed.** If the inequality symbol is or , draw the line solid.(3) If y < or y , shade the region BELOW the lineIf y > or y , shade the region ABOVE the lineIf x < or x , shade the region LEFT to the lineIf x > or x , shade the region RIGHT to the line
4 Example Graph y > x 4. Already in S-I form. The related equation is y = x 4. Use a dashed line because the inequality symbol is >. This indicates that the line itself is not in the solution set.(3) Determine which half-plane satisfies the inequality.y > x 4“>” shade above
5 Example Graph: 4x + 2y 8 1. Convert to S-I form: y -2x + 4 2. Graph the related equation.3. Determine which half-plane satisfies the inequality.“y ” shade below
6 Example Graph 2x – 4 > 0 . 1. One variable is missing. Solve it: 2. Graph the related equationx = 23. Determine which half-plane satisfies the inequality.“x >” shade the right.
7 Example Graph 8 - 3y 2 . 1. One variable is missing. Solve it: y 2 2. Graph the related equationy = 23. Determine the region to be shaded.“y ” shaded below
8 7.6 Systems of Linear Inequalities Graph the solution set of the system.First, we graph x + y 3 using a solid line.y - x + 3“above”Next, we graph x y > 1 using a dashed line.y < x – 1“below”The solution set of the system of equations is the region shaded both red and green, including part of the line x + y = 3.
9 ExampleGraph the following system of inequalities and find the coordinates of any vertices formed:We graph the related equations using solid lines. We shade the region common to all three solution sets.
10 Example continuedThe system of equations from inequalities (1) and (3):y + 2 = 0x + y = 0The vertex is (2, 2).The system of equations from inequalities (2) and (3):x + y = 2The vertex is (1, 1).To find the vertices, we solve three systems of equations. The system of equations from inequalities (1) and (2):y + 2 = 0x + y = 2The vertex is (4, 2).
11 SummaryTo graph a two-variable linear inequality, graph the related equation first (variable y must be solved) with appropriate boundary line:“<” and “>” use dash line“≤” and “≥” use solid line“y < …” and “y ≤ …” shade the region below“y > …” and “y ≥ …” shade the region above“x < …” and “x ≤ …” shade the region left“x > …” and “x ≥ …” shade the region rightWhen graphing the linear inequality system, follow the step 1 ~ 3 and choose the region shaded most.
12 Assignment6.5 P 363 #’s (even), (even), (even)7.6 P 435 #’s