Solving Linear Inequalities in Two Variables

Solving Linear Inequalities in Two Variables

Solving Linear Inequalities in Two Variables Adapted from Walch Education Key Concepts: Inequalities have infinitely many solutions and all the solutions need to be represented. This will be done through

the use of shading. A linear inequality in two variables has a half plane as the set of solutions. A half plane is a region containing all points that has one boundary, which is a straight line that continues in both directions infinitely. Key Concepts continued

Sometimes the line or the boundary is part of the solution; this means its inclusive. Inequalities that have greater than or equal to () or less than or equal to () symbols are inclusive. Use a solid line when graphing the solution to inclusive inequalities. Other times the line or boundary is NOT part of the solution; in other words, its non-inclusive. Inequalities that have

greater than (>) or less than (<) symbols are noninclusive. Use a dashed line when graphing the solution to non-inclusive inequalities. Key Concepts continued Graphing a Linear Inequality in Two Variables

Determine the symbolic representation (write the inequality using symbols) of the scenario if given a context. Graph the inequality as a linear equation. If the inequality is inclusive ( or ), use a solid line. If the inequality is non-inclusive (< or >), use a dashed line. Pick a test point above or below the line. If the test point makes the inequality true, shade the half plane that contains the test point.

If the test point makes the inequality false, shade the half plane that does NOT contain the test point. Quick Graphs Using Intercepts Standard Form of Linear Equations and Inequalities Linear equations can also be written as

ax + by = c, where a, b, and c are real numbers. An intercept is the point at which the line intersects (or intercepts) the x- or y-axis. Finding Intercepts The y-intercept is the point at which the line intersects the yaxis. The general coordinates for the y-intercept are (0, y).

To solve for the y-intercept in an equation, set x = 0 and solve for y. The x-intercept is the point at which the line intersects the xaxis. The general coordinates for the x-intercept are (x, 0). To solve for the x-intercept in an equation, set y = 0 and solve for x. Practice # 1

Graph the solutions to the following inequality. y>x+3 First, graph the inequality as a linear equation. (Since the inequality is non-inclusive, use a dashed line) y=x+3 The y-intercept is 3 and the slope is 1

We need to shade the appropriate half plane Choose (0, 0) because this point is easy to substitute into the inequality y>x+3 (0) > (0) + 3

0 > 3 This is false! Thanks for Watching !!!!! ~Dr. Dambreville

Recently Viewed Presentations

  • How do we find words in a dictionary?

    How do we find words in a dictionary?

    DICTIONARY LAYOUT Discuss with the person sitting next to you how the page is set out. Be ready to share your thoughts with the rest of the class. Features of Dictionaries The words are in columns The word you want...
  • The National Redress Scheme for survivors of institutional

    The National Redress Scheme for survivors of institutional

    Warren Strange August 2018. Outline. Today. Why we have a National Redress Scheme. An overview of the scheme and key issues in practice. knowmore's role and work to date with clients and accessing the NRS ... Experienced abuse after 1...
  • Academic Vocabulary How have you seen vocabulary taught?

    Academic Vocabulary How have you seen vocabulary taught?

    This is the Frayer Model example that you will get if you click on the example link. There are examples of academic vocabulary in Reading and Math grades K-6, with plans to add more as teachers are brought in this...
  • LWA SEE PROGRAM PROFESSIONAL DEVELOPMENT WORKSHOP 2017 LWA

    LWA SEE PROGRAM PROFESSIONAL DEVELOPMENT WORKSHOP 2017 LWA

    Text complexity exceeds ACSF Level 2 e.g. vocabulary, grammar. Task complexity exceeds ACSF Level 2 e.g. Q6, Q8, Q10, Q19. Simplify task for ACSF Level 2 use or apply to ACSF Level 3 with appropriate questions. Client Sample: Demonstrated. Client...
  • storm.cis.fordham.edu

    storm.cis.fordham.edu

    It has to do with logical form of the statements. Any two statements whose logical forms are related in same way as (1) and (2) would mean the say thing. Logical Equivalence. Compare truth tables for logic forms of two...
  • Fate and Transport of Pathogens in the Environment

    Fate and Transport of Pathogens in the Environment

    Dash board. Cup Holder. arithmetic average by sites. arithmetic average by sight & type of vehicle. 2% of vehicles had MRSA. 36% of vehicles had S. aureus. Ascending. Asending. Staph isolation according to sight percent
  • Chapter 18: Conflict and Absolutism

    Chapter 18: Conflict and Absolutism

    Absolutism. Ruler holds total power of government. Associated with divine rights of king. Seen in use in France, Spain, Prussia, and Russia ... Established the Prussian state. With limited natural boundaries, established large army. Created General War Commissariat.
  • Off-Axis response (1.49 keV) - NASA

    Off-Axis response (1.49 keV) - NASA

    Astro-E2 X-Ray Telescopes XRT Setup & Structure Performance Characteristics Effective Area Angular Resolution Optical Axes Field of View XRT Set up 5 XRT's on extended bench 4 on imagers with f=4.75m 1 on spectrometer with f=4.50m Same external dimension for...