1 / 11

Graphing and Solving Linear Inequalities in Two Variables

Learn how to graph and solve linear inequalities in two variables, and write inequalities from graphs. Practice examples are provided.

brandonb
Download Presentation

Graphing and Solving Linear Inequalities in Two Variables

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson Objective:I will be able to … • Graph and solvelinear inequalities in two variables • Language Objective: I will be able to … • Read, write, and listen about vocabulary, key • concepts, and examples

  2. Page 24 A linear inequality is similar to a linear equation, but the equal sign is replaced with an inequality symbol. A solution of a linear inequality is any ordered pair that makes the inequality true.

  3. y < 2x + 1 4 –3 < Example 1: Identifying Solutions of Inequalities Page 26 Tell whether the ordered pair is a solution of the inequality. (–2, 4); y < 2x + 1 4 2(–2) + 1 Substitute (–2, 4) for (x, y). 4 –4 + 1  (–2, 4) is not a solution.

  4. 5 4 + 1 55 > Your Turn 1 Page 26 Tell whether the ordered pair is a solution of the inequality. (4, 5); y > x + 1 y > x + 1 Substitute (4, 5) for (x, y).  (4, 5) is not a solution.

  5. Page 25

  6. Solve the inequality for y (slope-intercept form). Step 1 Graph the boundary line. Use a solid line for ≤ or ≥. Use a dashed line for < or >. Step 2 Shade the half-plane above the line for y > or ≥. Shade the half-plane below the line for y < or y ≤. Check your answer. Step 3 Page 25 Graphing Linear Inequalities

  7. Checky 2x –3 0 2(0) – 3  0 –3  Helpful Hint The point (0, 0) is a good test point to use if it does not lie on the boundary line. Example 2: Graphing Linear Inequalities in Two Variables Page 27 Graph the solutions of the linear inequality. y 2x –3 Step 1 The inequality is already solved for y. Step 2 Graph the boundary line y = 2x – 3. Use a solid line for . Step 3 The inequality is , so shade below the line.

  8. Step 2 Graph the boundary line y = – 4. Use a dashed line for <. –4x –4x Check y < – 4 y < – 4 –6 (1) – 4 –6 – 4 –6 < Your Turn 2 Page 28 Graph the solutions of the linear inequality: 4x –3y > 12 Step 1 Solve the inequality for y. 4x –3y > 12 –3y > –4x + 12 

  9. y-intercept: 1; slope: Replace = with > to write the inequality Example 3: Writing an Inequality from a Graph Page 28 Write an inequality to represent the graph. Write an equation in slope-intercept form. The graph is shaded above a dashed boundary line.

  10. y = mx + b y = –1x Page 29 Your Turn 3 Write an inequality to represent the graph. y-intercept: 0 slope: –1 Write an equation in slope-intercept form. The graph is shaded below a dashed boundary line. Replace = with < to write the inequality y < –x.

  11. Homework Assignment #35 • Holt 6-5 #12, 13, 15, 19-21, 23, 26, 63

More Related