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Understanding Linear Inequalities in Two Variables: Concepts and Applications

Linear inequalities in two variables represent relationships that cannot be expressed as equalities. They take the forms such as y > mx + b, y < mx + b, y ≥ mx + b, or y ≤ mx + b. Solutions to these inequalities are points (x, y) that satisfy the inequality. To graph these, one must determine whether to use solid or dashed lines and which side to shade. This concept is applicable in real-life scenarios, such as budgeting for movie tickets. For example, if you have a $30 gift certificate, how many shows can you attend?

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Understanding Linear Inequalities in Two Variables: Concepts and Applications

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  1. Algebra 2 – 2.6 LINEAR INEQUALITIES IN 2 VARIABLES

  2. Linear Inequality • An inequality that can be written in one of the following forms: y > mx + b y < mx + b y ≥ mx + b y ≤ mx + b • In other words, it is the same thing as a linear equation, but with a sign of inequality instead of an equals sign • BUT that sure makes for a big difference…

  3. Solution • A solution is a point, written as (x, y) that you could plug in and have a true statement of inequality • y > 2x + 3 Name three solutions.

  4. The three boxes ALGEBRA GRAPH LIST OF SOLUTIONS

  5. To graph • Graph the line just like always • Solid or dashed line? • Which side should you shade?

  6. Real World Application • Change our New York equations into inequalities

  7. COMPREHENSION QUESTIONS • You have a gift certificate for $30 to the local movie theater. Matinees are $8 and night shows cost $10. • Write and graph an inequality that represents the number of shows you can attend. • Give three possible combinations of shows that you could attend.

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