Graphing Systems of Linear Inequalities: Key Concepts and Examples

The video tutorial covers graphing systems of linear inequalities, explaining the steps involved, such as isolating y, plotting the y-intercept, and determining whether to use a solid or dotted line. It provides multiple examples, including special cases and scenarios with no solutions, to illustrate the concepts. The tutorial emphasizes understanding the solution set where the shaded regions of the inequalities overlap.

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

• Plot the y-intercept

• Isolate y

• Use rise over run

• Choose a solid or dotted line

When should you use a dotted line while graphing an inequality?

• When the inequality is equal to

• When the inequality is less than or equal to

• When the inequality is greater than or equal to

• When the inequality is greater than or less than

In the first example, what is the y-intercept of the inequality 2x + y > -4?

• -2

• -4

• 2

• 4

What does the symbol 'greater than' indicate about the shading of the graph?

• Shade under the line

• Shade over the line

• Shade to the left of the line

• Shade to the right of the line

In the second example, what happens to the inequality symbol when you divide by a negative number?

• It flips

• It becomes an equal sign

• It disappears

• It stays the same

What is the slope of the inequality y ≤ -1/4x + 3?

• -4

• -1/4

• 1/4

• 4

In the third example, what type of line is used for the inequality x > 2?

• Vertical line

• Curved line

• Diagonal line

• Horizontal line

What is the y-intercept of the inequality y < -2x - 4?

• -2

• -4

• 2

• 4

What does it mean when two inequalities have the same slope but different y-intercepts?

• The lines are perpendicular

• The lines intersect

• The lines overlap

• The lines are parallel

In the final example, what is the solution set for the system of inequalities if the lines are parallel and dotted?

• The area between the lines

• The area outside the lines

• There is no solution

• The lines themselves