7.8 notes[1]
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Transcript of 7.8 notes[1]
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Linear inequality in two variables The result of replacing the = sign in a linear equation with <, ≤, >, or ≥ .
Solution of an inequality in two variables An ordered pair (x, y) that produces a true statement when the values of x and y are substituted into the inequality.
Graph of an inequality in two variables The set of points that represent all solutions of the inequality
Half-plane Either half of the coordinated plane that is divided by the boundary line of a linear inequality.
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Example 1: Check solutions of a linear inequality
Tell whether the ordered pair is a solution of 2x – 3y > 5. a. ( 4, 1 ) b. ( 2, -2)
SOLUTION a. ( 4, 1 ) Step 1 Write the inequality.
Step 2 Substitute the values of the ordered pair.
Step 3 Simplify
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Example 2: Graph a linear inequality in two variables
Graph the inequality Graph the inequality yy>4>4xx-2-2SOLUTION Step 1 Graph the equation. Step 2 Test a point not on the boundary line.
Step 3 Shade the half-plane containing the point if the ordered pair is a solution of the inequality. Shade the other half-plane if the ordered pair is not a solution.
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Example 3: Graph a linear inequality in one variableGraph the inequality y≥-4.
SOLUTIONStep 1 Graph the equation Step 2 Test a point
Step 3 Shade
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TRY ON YOUR OWNTRY ON YOUR OWNGraph the inequality.Graph the inequality.2. 2. yy<3<3xx-4 -4
3. x< -2
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Example 4: Multiple Choice Practice
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HOMEWORK: Textbook p. 429- # 3-6 all, 19-22 all