Half Planes and Linear Inequalities

What is ...........the set of two or more linear inequalities involving the same variables x and y.

• Linear Function

• System of Linear Inequalities

• System of Equations

• Boundary Line

a line plotted on a coordinate graph that divides the graph (or plane) into two half‐planes. Can be dashed or solid.

• Linear Function

• Slope

• Y-Intercept

• Boundary Line

What is the definition for Solution Set?

•  

  the relationship between two values showing if one is less than, greater than, or simply not equal to another value. (<, >, ≤ or ≥)

   

   

   

• a function that represents a straight line on the coordinate plane.

• a mathematical expression in which two expressions are compared using the inequality symbol. Almost the same as a linear equation, except the equals sign is replaced with an inequality.

• the set of two or more linear inequalities involving the same variables x and y.

What is the definition for Linear Inequality?

•  

  the relationship between two values showing if one is less than, greater than, or simply not equal to another value. (<, >, ≤ or ≥)

   

   

   

• a function that represents a straight line on the coordinate plane.

• a mathematical expression in which two expressions are compared using the inequality symbol. Almost the same as a linear equation, except the equals sign is replaced with an inequality.

• the set of two or more linear inequalities involving the same variables x and y.

Which of the following inequalities matches the graph?

• y ≤ 3/4x + 5

• y ≥ 3/4x + 5

• y < 3/4x + 5

• y > 3/4x + 5

Which point below is NOT part of the solution set?

• (0, 0)

• (-10, 20)

• (3, 5)

• (0, -2)

Which inequality matches the picture shown?

• y < -1/2 x + 5

• y < -1/2 x + 5

• y > -1/2 x + 5

• y > -1/2 x + 5

Which of the following inequalities matches the graph?

• y > 2x - 2

• y < 2x - 2

• y ≥ 2x - 2

• y ≤ 2x - 2

Select the correct graph for each inequality.

• A

• B

• C

• _D

Which of the following equations match the given graph?

• y ≤ -3/4 x + 3

• y ≥ -3/4 x + 3

• y < -3/4 x + 3

• y > -3/4 x + 3