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Section 7 – 5 Graphing Linear Inequalities

Section 7 – 5 Graphing Linear Inequalities. Objectives: To graph inequalities To write and use linear inequalities when modeling real-world situations. Linear Inequality :. An inequality containing two variables, that describes a region of the coordinate plane that has a boundary line.

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Section 7 – 5 Graphing Linear Inequalities

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  1. Section 7 – 5Graphing Linear Inequalities Objectives: To graph inequalities To write and use linear inequalities when modeling real-world situations

  2. Linear Inequality: An inequality containing two variables, that describes a region of the coordinate plane that has a boundary line. Solution of a Linear Inequality: The coordinate of the points that make the inequality true.

  3. HELPFUL HINTS WHEN GRAPHING LINEAR INEQUALITIES: • Write the equation in slope-intercept form (y=mx+b) • Graph the inequality as if it was an equation in slope-intercept form. • Use a dotted line for < or >, Use a solid line for ≤ or ≥ • Shade on top for > or ≥ • Shade on bottom for < or ≤. • Check your work by choosing a point in the shaded region, if the statement is true when you simplify, you shaded the correct way!

  4. Example 1 Graphing an Inequality A) Graph y < 2x + 3.

  5. B) Graph

  6. C) Graph y > -2x + 1

  7. Example 2 Rewriting to Graph an Inequality A) Graph 3x – 5y ≤ 10.

  8. B) Graph 4x – 3y > 9

  9. C) Graph 6x + 8y ≥ 12

  10. Example 3 Horizontal & Vertical Lines A) Graph y < 3 B) Graph x ≤ 2

  11. Homework:Textbook Page 373; #2 – 22 Even

  12. Section 7 – 5Continued… Objectives: To write and use linear inequalities when modeling real-world situations

  13. WARM UP For each linear inequality, decide where you would shade. • y < 4x – 2 • 2x – 4y ≤ 8 • Write the inequality for the graph. • Jan’s Graph of the inequality 4x + 6y > 12 is shown below. What is wrong with the graph?

  14. Example 3 Horizontal & Vertical Lines A) Graph y < 3 B) Graph x ≤ 2

  15. Example 4 Real-World Problem Solving A) Suppose your budget for a party allows you to spend no more than $12 on peanuts and cashews. Peanuts cost $2/lb and cashews cost $4/lb. Find three possible combinations of peanuts and cashews you can buy.

  16. B) Suppose you plan to spend no more than $24 on a meat cookout. At your local market, hamburger costs $3.00/lb and chicken wings cost $2.40/lb. Find three possible combinations of hamburger and chicken wings you can buy.

  17. C) Suppose your budget for the Freshman Dance allows you to spend no more than $24 for decorations for a party. Streamers cost $2 a roll and tablecloths cost $6 each. Find three possible combinations of streamers and tablecloths you can buy.

  18. Homework:Complete Practice Ditto

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