Presentation on theme: "Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from."— Presentation transcript:
Graphing Inequalities of Two Variables Recall… Solving inequalities of 1 variable: x + 4 ≥ 6 x ≥ 2 [all points greater than or equal to 2] Different from x + 4 = 6 x = 2 [only 1 solution] Likewise, inequalities w/ 2 variables have more than 1 solution…
Graphing Inequalities of Two Variables (1) Graph of linear equation separates coordinate plane into 3 parts: - Points on one side of the line - Points on boundary line (dashed for ˂ or ˃, solid line for ≥ or ≤). - Points on other side of the line (2) When the equality symbol is replaced w/ an inequality symbol, the statement becomes a linear inequality. Any ordered pair that makes the linear inequality true is a solution. (3) To graph linear inequalities: (A) Graph boundary line (determine whether line is dashed or solid based on inequality symbol). (B) Choose any point not on line, and substitute x- & y- values in linear inequality to see if the ordered pair is a solution. (C) If ordered pair is a solution, shade that side of the boundary line; if not, shade other side (verify w/ another ordered pair).
Graphing Inequalities of Two Variables Example Problems: p. 570, ex. 5, 6, 7, 14, 15, 17
Graphing Inequalities of Two Variables Think & Discuss (1)Compare the uses of an open circle, a closed circle, a dashed line, and a solid line when graphing inequalities. (2)Explain how you can tell if a point on the line is a solution of the inequality. (3)Name a linear equation for which the graph is a horizontal dashed line and all points below it. HW: p. 570-571 – ex. 16, 18, 20-28