Exploring Systems of Linear Inequalities

What is a system of linear inequalities?

• A set of parallel lines

• A single linear equation

• Two or more linear inequalities graphed together

• A quadratic equation

What is the solution to a system of linear inequalities?

• The area below the lines

• The area above the lines

• The overlapping region of shaded areas

• The intersection point of the lines

When graphing a linear inequality, what does a dashed line indicate?

• The line is horizontal

• The inequality includes the line

• The inequality does not include the line

• The line is vertical

In the first example, what is the slope of the top inequality?

• -1

• 2

• 1

• 0

In the first example, where do we shade for the bottom inequality?

• Below the line

• To the left of the line

• On the line

• Above the line

In the second example, what is the slope of the top inequality?

• 1/3

• -1/3

• -3

• 3

In the second example, what type of line is used for the bottom inequality?

• Vertical line

• Dashed line

• Solid line

• Horizontal line

In the third example, what is the y-intercept of the bottom equation?

• 2

• -2

• 1

• -1

In the third example, what do we do when dividing by a negative number?

• Keep the inequality the same

• Flip the inequality sign

• Change the slope

• Change the y-intercept

In the final example, what is the slope of the bottom equation?

• 1

• -3

• 3

• -1