Understanding Linear Inequalities

This video tutorial introduces linear inequalities in two variables, starting with a review of linear equations. It explains how to graph linear equations and test ordered pairs to see if they satisfy the equation. The tutorial then transitions to linear inequalities, showing how to form them from equations by replacing the equal sign with an inequality symbol. It covers graphing linear inequalities, including shading regions and using solid or dashed lines to indicate whether the line is part of the solution set.

What is the primary difference between a linear equation and a linear inequality?

• A linear equation can only have positive solutions, while a linear inequality can have negative solutions.

• A linear equation has no variables, while a linear inequality does.

• A linear equation uses an equal sign, while a linear inequality uses an inequality symbol.

• A linear equation is always graphed as a curve, while a linear inequality is a straight line.

What does the slope of a line represent in a linear equation?

• The steepness and direction of the line.

• The point where the line crosses the x-axis.

• The total number of solutions for the equation.

• The point where the line crosses the y-axis.

What is the significance of the vertical intercept in a linear equation?

• It determines the slope of the line.

• It is the point where the line crosses the y-axis.

• It indicates the number of solutions.

• It shows the direction of the line.

If a point is not on the line of a linear equation, what does it imply?

• The point does not satisfy the equation.

• The point satisfies the equation.

• The point is the origin.

• The point is the slope.

How is a linear inequality formed from a linear equation?

• By dividing both sides by a constant.

• By multiplying both sides by a variable.

• By replacing the equal sign with an inequality symbol.

• By adding a constant to both sides.

What does a solid line indicate when graphing a linear inequality?

• The inequality is undefined.

• The inequality is strict (less than or greater than).

• The inequality includes the line (less than or equal to, greater than or equal to).

• The inequality has no solution.

What is the purpose of shading a region on the graph of a linear inequality?

• To mark the origin.

• To indicate the slope of the line.

• To show the solution set of the inequality.

• To highlight the x-intercept.

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

• The inequality is equal to zero.

• The inequality has no solution.

• The inequality is strict and does not include the line.

• The inequality includes the line.

How do you determine which side of the line to shade for a linear inequality?

• By checking the x-intercept.

• By using a test point and checking if it satisfies the inequality.

• By finding the slope of the line.

• By calculating the y-intercept.

What happens if a test point satisfies the inequality?

• Shade the opposite side of the test point.

• Shade the same side as the test point.

• Shade both sides of the line.

• Do not shade any side.