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6.5 Graphing Linear Inequalities in Two Variables

6.5 Graphing Linear Inequalities in Two Variables. Wow, graphing really is fun!. What is a linear inequality?. A linear inequality in x and y is an inequality that can be written in one of the following forms. a x + b y < c a x + b y ≤ c a x + b y > c a x + b y ≥ c.

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6.5 Graphing Linear Inequalities in Two Variables

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  1. 6.5 Graphing Linear Inequalities in Two Variables Wow, graphing really is fun!

  2. What is a linear inequality? • A linear inequality in x and y is an inequality that can be written in one of the following forms. • ax + by < c • ax + by≤ c • ax + by > c • ax + by ≥ c

  3. An ordered pair (a, b) is a solution of a linear equation in x and y if the inequality is TRUE when a and b are substituted for x and y, respectively. • For example: is (1, 3) a solution of 4x – y < 2? • 4(1) – 3 < 2 • 1 < 2 This is a true statement so (1, 3) is a solution.

  4. Check whether the ordered pairs are solutions of 2x - 3y ≥ -2.a. (0, 0) b. (0, 1) c. (2, -1)

  5. Graph the inequality 2x – 3y ≥ -2 Every point in the shaded region is a solution of the inequality and every other point is not a solution. 3 2 1 -3 -2 -1 1 2 3 4 -1 -2 -3

  6. Steps to graphing a linear inequality: • Sketch the graph of the corresponding linear equation. • Use a dashed line for inequalities with < or >. • Use a solid line for inequalities with ≤ or ≥. • This separates the coordinate plane into two half planes.

  7. Test a point in one of the half planes to find whether it is a solution of the inequality. • If the test point is a solution, shade its half plane. If not shade the other half plane.

  8. Sketch the graph of 6x + 5y ≥ 30 • Write in slope- intercept form: y ≥ -6/5x + 6 This will be a solid line. • Test a point. (0,0)6(0) + 5(0) ≥ 300 ≥ 30 Not a solution. • Shade the side that doesn’t include (0,0). 6 4 2 -6 -4 -2 2 4 6 8 -2 -4 -6

  9. Sketch the graph y < 6. • This will be a dashed line at y = 6. • Test a point. (0,0)0 < 6 This is a solution. • Shade the side that includes (0,0). 6 4 2 -6 -4 -2 2 4 6 8 -2 -4 -6

  10. Sketch the graph of 2x – y ≥ 1 • Write in slope- intercept form: y = 2x – 1 This will be a solid line. • Test a point. (0,0)2(0) - 0 ≥ 10 ≥ 1 Not a solution. • Shade the side that doesn’t include (0,0). 3 2 1 -3 -2 -1 1 2 3 4 -1 -2 -3

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