Algebra 6.5 Graphing Linear Inequalities

Linear Inequality A linear inequality in 2 variables, x and y looks like a linear equation except that it has an inequality symbol instead of = Has an infinite number of solutions (x,y) that are points in one half of the coordinate plane Examples: y > 2x + 3 y ≤ -3x - 1

Graph of Linear Inequality Looks like this (shaded half-plane) The solutions are all the points in the shaded region

Steps to Graphing (After Writing in Slope-Int. Form) 1.Graph the corresponding equation Use dashed line for > or < Use solid line for ≥ or ≤ 2.Shade the appropriate half-plane Shade above for > or ≥ Shade below for < or ≤ 3.Test (0, 0).

Example Graph 2x + y > 3 (hint: rewrite the equation 2x + y > 3 in slope- intercept form so that it is easy to graph.) y > -2x + 3 dashed line

Example Graph y > -2x + 3 shade above

Example Test (0,0): 2x + y > 3  original inequality 2(0) + 0 >3 0 > 3 (0, 0) is not a solution. It should not be in the shaded region. It is not. The correct half-plane is shaded.

You try! Graph 3y – x ≤ -12 Rewrite in SI form:3y ≤ x - 12 y ≤ x - 4 What kind of line – dashed or solid? Shaded above or below the line?

You try! Graph Solid line, shaded below y ≤ x - 4

Practice identifying above ( >, ≥) vs. below ( <, ≤) shading above below above below = left (less than) above = right (greater than) above below y > 4 y < 6 x < 3 x > -2

Homework pg. 363 # 39-56, 61-63