Graphing Systems of Inequalities in Standard Form

The video tutorial covers lesson seven on systems of inequalities in standard form. It reviews inequality symbols and graphing basics, then provides four detailed examples of solving and graphing systems of inequalities. Each example demonstrates how to solve for y, graph the inequalities, and identify the solution region where the shaded areas overlap. The lesson emphasizes the importance of flipping the inequality symbol when dividing by a negative and highlights the solution region as the area of overlap.

What is the first step when graphing an inequality that is not solved for y?

• Solve for y

• Draw a dashed line

• Flip the inequality symbol

• Shade the region above the line

What happens to the inequality symbol when you multiply or divide by a negative number?

• It becomes an equal sign

• It flips

• It disappears

• It stays the same

In Example 1, what type of line is used to graph the inequality 9x + 3y ≤ 6?

• Dashed line

• Solid line

• Vertical line

• Horizontal line

Where do you start graphing the line for the inequality y > x?

• At the point (1,1)

• At the origin

• At the x-intercept

• At the y-intercept

In Example 2, what is the slope of the line for the inequality -y ≤ 3x - 2 after solving for y?

• 1/2

• -1/2

• -3

• 3

What type of line is used to graph the inequality x - 2y > 4?

• Horizontal line

• Vertical line

• Solid line

• Dashed line

In Example 3, what is the y-intercept of the line for the inequality 12x - 4y > 8 after solving for y?

• 3

• 2

• -2

• -3

What type of line is used to graph the inequality x > 4?

• Solid vertical line

• Dashed vertical line

• Dashed horizontal line

• Solid horizontal line

In Example 4, what is the slope of the line for the inequality x + 3y > 9 after solving for y?

• 3

• -1/3

• 1/3

• -3

What is the solution region for a system of inequalities?

• The area below the second line

• The area above the first line

• The area where the shaded regions overlap

• The area where the lines intersect