2.8 Graph Linear Inequalities in Two Variables

In this lesson you will: Graph linear inequalities in two variable. Use linear inequalities to solve real-life problems.

A Linear Inequality in two variables can be written in one of these forms: Ax+By<C Ax+By>C An ordered pair (x,y) is a solution of a linear inequality if the inequality is true when the values of x an y are substituted into the inequality. For example: (-6,2) is a solution of y>3x-9 because 2>3(-6)-9 is a true statement.

Which of these ordered pairs are solutions of 2x + 3y > 5? (0,1)? (4,-1)? (2,1)?

Graph y < 2x Test a point in one of the half-plane ( test (5,0)) Graph the boundry line y = 2x Test a point in one of the half-plane ( test (5,0)) Why is the “boundry line” “dashed” rather than solid? Why is the “right” shaded rather than the “left”?

Graph the linear inequality 2x-5y>10 Graph the “boundary line” 2x-5y=10. Test a point in one of the half-planes (e.g. (0,0))