Lesson 6.7 Graph Linear Inequalities in Two Variables Essential Question: How do you graph linear inequalities in two variables?

Before we start… Graph 𝑦=𝑥+1 Where do you think you would find solutions to 𝑦>𝑥+1? Where do you think you would find solutions to 𝑦<𝑥+1?

What is a linear inequality in two variables? It looks just like a linear equation but contains an inequality symbol instead.

What is a solution of a linear inequality in two variables? An ordered pair (x, y) is a solution of a linear inequality in two variables if the inequality is true when the values of x and y are substituted into the inequality.

Which ordered pair is not a solution of 𝑥−3𝑦≤6? b) 6,−1 c) 10,3 d) −1,2

Which ordered pair is a solution of 3𝑥+4𝑦>8? a) 6,−3 b) 0,2 c) −2,−1 d) −3,5

Tell whether the ordered pair is a solution of −𝑥+2𝑦<8. a) 0,0 b) 0,4 c) 3,5 d) −3,1

Tell whether the ordered pair is a solution of 5𝑥−2𝑦≤6. a) 0,−4 b) 2,2 c) −3,8 d) −1,−7

What is the graph of a linear inequality in two variables? The set of all points in a coordinate plane that represent solutions of the inequality.

How do you interpret graphs of linear inequalities in two variables? A dashed boundary line means that points on the line are not solutions. A solid boundary line means that points on the line are solutions.

How do you graph a linear inequality in two variables? Graph the boundary line. Use a dashed line for < or > Use a solid line for ≤ or ≥ Shade the half plane that contains the solutions. Shade above the line if it’s greater than Shade below the line if it’s less than Pick a test point to verify your solution.

What about linear inequalities in one variable? The same rules apply for one variable inequalities as two variable inequalities. Remember x results in a vertical line and y results in a horizontal line.

How do you graph linear inequalities in two variables?

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