Section 2.8 – Graphing Linear Inequalities EQ: How can I interpret a linear inequality in order to graph?

Linear Inequality resembles a linear equation, but with an inequality instead of an equals symbol. For example, y > –3x – 2 versus y = –3x – 2. *The graph of the inequality y > –3x – 2 is shown at the right as a shaded region. *Every point in the shaded region satisfies the inequality. The graph of y = –3x – 2 is the boundary of the region. It is drawn as a dashed line to show that points on the line do not satisfy the inequality. If the symbol was ≤ or ≥, then the points on the boundary would satisfy the inequality, so the boundary would be written as a solid line.

Steps to Graphing Linear Inequalities Write the inequality in slope intercept form. Graph the inequality Connect the dots: With a solid line if ≤ or ≥ With a dashed line is < or > Shade: Above the line if > or ≥ Below the line if < or ≤

Example 1 Graph x – 2y < 4 Step 1: Put equation in slope – intercept form −2𝑦<−𝑥+4 𝑦> 1 2 𝑥−2 Step 2: Graph Step 3: Shade according to inequality Must flip sign since you are dividing by a negative

Example 2 Graph 2x + 5y > 10 5𝑦≥−2𝑥+10 𝑦≥− 2 5 𝑥+2

Example 3 Graph x – y > –2 −𝑦>−𝑥−2 𝑦<𝑥+2

You Try! Graph 9x + 3y – 6 ≤ 0 Do on your own!

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Homework: pg. 119 #8 – 11, 16, 17, 21, 24