Graphing Linear Inequalities Concepts

This video tutorial teaches how to find solutions to simultaneous linear inequalities by graphing. It begins with a review of systems of equations and their solutions, emphasizing the point of intersection. The tutorial then explains how to graph inequalities on a number line using open and closed points. It covers graphing linear inequalities with boundary lines and shading the correct half-plane. The video also demonstrates graphing two inequalities on the same line and finding the solution region. Finally, it shows how to find solutions to systems of linear inequalities by graphing and shading the appropriate regions.

What is the significance of the point where two lines intersect?

• It is the endpoint of the lines.

• It is the starting point of the lines.

• It is a solution to both equations.

• It is the midpoint of the lines.

How is an inequality in one variable represented on a number line?

• As a solid line with no points.

• As a dashed line with no points.

• As a circle with no line.

• As a ray with an open or closed point.

What does a broken boundary line indicate in a graph of a linear inequality?

• The line is a solid boundary.

• The line is the only solution.

• The points on the line are not solutions.

• The points on the line are solutions.

In the inequality y > 2x - 3, which region should be shaded?

• The region above the line.

• The region below the line.

• No region should be shaded.

• The line itself.

What is a common mistake when shading regions for inequalities?

• Shading the entire graph.

• Shading the wrong side of the boundary line.

• Shading only the boundary line.

• Not shading at all.

How do you represent x > -3 on a number line?

• With a closed point at -3 and shading to the left.

• With an open point at -3 and shading to the left.

• With a closed point at -3 and shading to the right.

• With an open point at -3 and shading to the right.

What does the double-shaded area represent when graphing two inequalities?

• The area outside the solution.

• The area with no solutions.

• The solution to both inequalities.

• The solution to only one inequality.

When graphing y ≥ 12x + 2, which side of the line should be shaded?

• Below the line.

• Above the line.

• On the line.

• No shading is needed.

What type of line is used to graph y < -25x + 5?

• A solid line.

• A broken line.

• A dotted line.

• A thick line.

What is the final step in finding the solution to a system of linear inequalities?

• Shading the regions.

• Solving the equations algebraically.

• Graphing the lines.

• Identifying the double-shaded area.