Algebra 6 5 Graphing Linear Inequalities Linear Inequality

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

Example • Graph y > -2 x + 3 shade above

Example • Test (0, 0): 2 x + y > 3 2(0) + 0 >3 0>3 original inequality (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 3 y – x ≤ -12 Rewrite in SI form: 3 y ≤ x - 12 y ≤ x-4 What kind of line – dashed or solid? Shaded above or below the line?

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

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

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