Graphing Linear Inequalities In Two Variables Worksheet Example 3 8 2 3 8 2 Graph the solution set 2x 5y 10 2 x 5 y 10 Solution Here the boundary is defined by the line 2x 5y 10 2 x 5 y 10 Since the inequality is inclusive we graph the boundary using a solid line In this case graph the boundary line using intercepts Figure 3 8 9 3 8 9
Graphing Linear Inequalities Worksheets This ensemble of printable graphing linear inequalities worksheets drafted for high school students assists in comprehending the use of inequalities when there is a range of possible answers Identify the shaded region and the type of boundary line as dashed or solid complete the inequality check if The method of graphing linear inequalities in two variables is as follows Graph the boundary line consider the inequality as an equation that is replace the inequality sign with an equal sign If the inequality is or draw the boundary line solid This means that points on the line are solutions and are part of the graph
Graphing Linear Inequalities In Two Variables Worksheet
Graphing Linear Inequalities In Two Variables Worksheet
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2 9 Graphing Linear Inequalities In Two Variables Ms Zeilstra s
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A linear inequality is an inequality that can be written in one of the following forms Ax By C Ax By C Ax By C Ax By C A x B y C A x B y C A x B y C A x B y C Where A and B are not both zero Recall that an inequality with one variable had many solutions If the test point is a solution shade in the side that includes the point If the test point is not a solution shade in the opposite side Example 3 5 13 3 5 13 Graph the linear inequality x 2y 5 x 2 y 5 Answer Example 3 5 14 3 5 14 Graph the linear inequality 2x 3y 6 2 x 3 y 6
5x y y 5 y The y y 0 and disappears 5x 5 y And subtract 5 from both sides 5x 5 y Now reverse the sides and reverse the sign y 5x 5 So we now the slope is 5 and y intercept is 0 5 So graph that line solid because it is also to and shade everything below the line since it is also For example the equation 3x 12 becomes x 4 because you have divided both sides by a negative value To check if this is correct replace x with a value that is less than 4 such as 5 Then evaluate the original equation to see if it makes sense In this case if you insert a 5 in place of x in the equation 3x 12 you get 15 12
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The graph of a two variable linear inequality looks like this A coordinate plane with a graphed system of inequalities The x and y axes both scale by two There is a solid line representing an inequality that goes through the points zero two and three zero The shaded region for the inequality is below the line A linear inequality in two variables x and y can be written as ax by c ax by c ax by c ax by c where a b and c are real numbers A solution of a linear inequality in two variables is an ordered pair x y that makes the inequality true
STANDARD A REI D 12 AI Graph the solutions to a linear inequality in two variables as a half plane excluding the boundary in the case of a strict inequality and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half planes Answer The steps are the same for nonlinear inequalities with two variables Graph the boundary first and then test a point to determine which region contains the solutions Example 2 7 5 Graph the solution set y x 2 2 1 Solution The boundary is a basic parabola shifted 2 units to the left and 1 unit down
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Graphing Linear Inequalities In Two Variables Worksheet - If the test point is a solution shade in the side that includes the point If the test point is not a solution shade in the opposite side Example 3 5 13 3 5 13 Graph the linear inequality x 2y 5 x 2 y 5 Answer Example 3 5 14 3 5 14 Graph the linear inequality 2x 3y 6 2 x 3 y 6