2.8 Graphing Linear Inequalities in Two Variables

Graphing Vertical and Horizontal lines We graph the inequalities the same as equations, but with a couple of differences…. Put in form of y = mx + b Find the slope and the y-intercept

Dashed or Solid If an inequality has a < or >, then draw a dashed line. If an inequality has a , then draw a solid line.

Shading < and is shaded below the line > and is shaded above the line.

If you are not sure which side of the line to shade, plug in any point as a test. You need to use a point that is NOT on the line. (0,0) are (1,1) are usually good test points to use, as long as the point you choose is not on the line.

Example: y < x + 3 slope is 1, y intercept is at (0,3) Line is dashed because it is <, The line is shaded below and to the right of the line. Any and All of the points in the shaded area are part of the solution.

Example: y ≥ 2x -1 slope is 2, y intercept is at (0,-1) Line is solid because it is ≥, Plug in (0,0) as a test point: 0 ≥ 0 – 1 ---TRUE, so (0,0) is in the shaded area. Shaded above and to the left of the line.

y > -x + 2 Plug in (0,0) 0 > 0 + 2 0 > 2 NOT TRUE

Lines with Slope Decide whether your line is solid or dashed. Rewrite the inequality as an equation in y = mx + b form. Graph using the y-intercept and slope. Plug a test point {usually (0, 0)} to determine on which side of the line you should shade.

Classwork Practice Page 118, #8-16

Graphing Absolute Value Inequalities y < |x-2| + 3 This is in the form y = a |x-h| + k So the vertex is (2,3) and the right side of the “V” has a slope of 1. Since y < |x-2| + 3 Shade below the graph

Graphing Absolute Value Inequalities y ≥ ½ |x+2|

Graphing Absolute Value Inequalities y > -2 |x-1| - 4

Classwork Text page 118, #8-16 All, and #19-29 odd