Exploring Linear Inequalities Concepts

The video tutorial explains linear inequalities, merging concepts from linear equations and inequalities. It covers graphing linear inequalities on a coordinate plane, identifying solutions, and understanding the significance of shading and line types. The tutorial includes examples to illustrate graphing and verifying solutions, emphasizing the importance of slope-intercept form and inequality symbols.

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

• Linear inequalities include an inequality symbol instead of an equal sign.

• Linear inequalities use a different graphing plane.

• Linear inequalities cannot be graphed.

• Linear inequalities use only one variable.

What is the slope of the line represented by the inequality y > x - 3?

• 0

• -3

• 1

• 3

Why is a dotted line used when graphing the inequality y > x - 3?

• Because the inequality includes the equal sign.

• To indicate that the line itself is not part of the solution set.

• To differentiate it from quadratic inequalities.

• Because it represents a decreasing function.

Which of the following points is a solution to the inequality y > x - 3?

• (1, 0)

• (3, 1)

• (-3, -3)

• (0, 0)

If an inequality is 'greater than', where should the graph be shaded?

• Only on the line.

• Below the line.

• No shading is required.

• Above the line.

What does an open circle on a number line in the context of inequalities represent?

• The number is part of the solution set.

• The number is not part of the solution set.

• The inequality is undefined at that number.

• The graph is discontinuous at that point.

What does a solid line in a graph of an inequality indicate?

• The function is undefined.

• The inequality includes 'or equal to'.

• The inequality is non-linear.

• The line is not part of the solution set.

When graphing the inequality 4x - y > 2, why do we start by translating it to slope-intercept form?

• To make it easier to graph by identifying the slope and y-intercept.

• To simplify the equation for integration.

• Because it cannot be graphed in any other form.

• To determine the maximum and minimum values.

How do you verify if a point is a solution to an inequality?

• Graph the point and see if it lies on the line.

• Check if the point lies above the line regardless of the inequality.

• Substitute the point into the inequality and check if the inequality holds.

• Only substitute the x-value into the inequality.

What is the y-intercept of the inequality after translating 4x - y > 2 into slope-intercept form?

• 2

• -2

• 4

• -4