2.8 Graph Linear Inequalities in Two Variable

Types of Two Variable Inequalities: Linear Inequality: y < mx + b Ax + By ≥ C Absolute Value Inequality: y > a|x – h| + k

Solutions: (x,y) ordered pairs that are true for the inequality when substituted into the inequality. Boundary Line: dotted or solid : dotted lines doe not contain solutions : solid lines do contain solutions Region: is the shaded area of the graph. : contains solutions to the inequality.

Understanding the Symbols: Y < means dotted line and shade below Y > means dotted line and shade above Y ≤ means solid line shade below Y ≥ means solid line shade above X < vertical line, dotted, shade left X > vertical line, dotted, shade right X ≤ vertical line, solid, shade left X ≥ vertical line, solid, shade right

Graph a linear Inequality in one variable Horizontal Line (EX 1) y < 4 Line type: Region: Vertical Line (EX 2) x ≥ 2 Line type: Region:

Graph a Linear Inequality in two Variable Slope Intercept Form (EX 3) y > - 2x Line type: Region Graph:

Standard Form: (EX 4) 5x – 2y ≤ - 10 Identify the x and y intercepts: x-int: (, ) y-int: (, ) Sub in (0,0) to identify the region. Graph:

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Graph an Absolute Value Inequality (EX 5) y > -2|x – 3| + 4 Vertex: (, ) open: slope: type of line: region: (shade above the vertex or below) Graph: