Graphing Inequalities Eric Hoffman Algebra II PLHS Sept. 2007
Key Topics Graphing Inequalities: to graph an inequality you graph “boundary line” then shade the appropriate region Boundary Line: the line that is the boundary for the shaded region Boundary Line
Key Topics If the inequality is a “≤” or “≥” then the boundary line is solid If the inequality is a “<” or “>” then the boundary line is dashed
Steps For Graphing an Inequality Step 1: Determine whether the boundary line is dashed or solid Step 2: Graph the boundary line Step 3: Choose a point on either side of the boundary line and check to see if the values satisfy the inequality Step 4: Shade the side of the boundary line that satisfies the inequality
Graphing an Inequality Graph the inequality 2x + 3y > 6 3y > -2x + 6 y > (-2/3)x + 2 Graph: y = (-2/3)x + 2 Choose any point: (3,3) 3 > (-2/3)(3) + 2 2 > (-2) + 2 2 > 0 Tells us the boundary line is dashed (3,3) is just a random point This is true, so we shade the side of the boundary line that this point is on
True, so shade this region Key Topics Graph the inequality 3y + 6x ≥ 9 y ≥ -2x + 3 Check point: (2,1) 1 ≥ -2(2) + 3 1 ≥ -1 y = -2x + 3 True, so shade this region
Graphing Absolute Value Inequalities Same method as graphing regular inequalities The graph of the absolute value of a linear equation will always look like a “V” If you have trouble graphing absolute values, just plot points by picking different values for x
Absolute Value Inequality There are basically two regions, region 1 is all the points where y is greater than, and region 2 is all the points where y is less than 1 y = | x – 1| 2 2
(0,3) satisfies the inequality, so shade this region Key Topics Graph y ≥ | 3x + 2 | Boundary line: y = | 3x + 2 | Choose a point: (0,0) Choose another point: (0,3) (0,0) doesn’t satisfy the inequality so you can’t shade the region that it is in y = | 3x + 2 | (0,3) satisfies the inequality, so shade this region
Homework Pg. 98 14 – 28 even, 32 – 37 all 14 problems You will need graph paper (provided)