Graphing Linear Inequalities Concepts

This video tutorial covers systems of linear inequalities, including checking solutions, graphing, and writing systems from graphs. It also explores real-life applications, demonstrating how to determine solutions and graph systems. The tutorial explains the no solution case and provides examples of deriving systems from graphs.

What is a system of linear inequalities?

• A set of equations with no variables

• A set of quadratic equations

• A set of two or more linear inequalities in the same variables

• A single linear equation

How do you determine if an ordered pair is a solution to a system of linear inequalities?

• By checking if it satisfies at least one inequality

• By checking if it satisfies only the first inequality

• By checking if it satisfies all inequalities in the system

• By checking if it satisfies none of the inequalities

What is the first step in graphing a system of linear inequalities?

• Graph each inequality in the same coordinate plane

• Shade the entire graph

• Solve each inequality algebraically

• Find the intersection of the half-planes

When graphing y is less than or equal to 3, what type of line is used?

• Solid line

• Dashed line

• No line

• Dotted line

What does a dashed line represent in the graph of a linear inequality?

• The inequality is quadratic

• The inequality includes the line

• The inequality is undefined

• The inequality does not include the line

How do you determine the inequality symbol for a line when writing a system from a graph?

• By the color of the line

• By the slope of the line

• By the position of the shaded region relative to the line

• By the length of the line

In a real-life scenario, if you have at most 8 hours to spend at two locations, how would you represent this as an inequality?

• x + y > 8

• x + y < 8

• x + y ≤ 8

• x + y ≥ 8

If you want to spend more than 4 hours at the beach, how would you represent this in an inequality?

• y ≥ 4

• y > 4

• y ≤ 4

• y < 4

What does the shaded region in a graph of a system of linear inequalities represent?

• The area where no solutions exist

• The area where all solutions exist

• The area where only one solution exists

• The area where the graph is undefined

How can you determine the feasible region in a system of linear inequalities?

• By shading the entire graph

• By drawing only one line

• By ignoring the inequalities

• By finding the intersection of all shaded regions