Graphing Inequalities and Their Properties

The video tutorial covers solving and graphing two inequalities. The instructor first addresses technical difficulties and then proceeds to solve the first inequality by rearranging it into a suitable format for graphing. The process involves isolating the variable y and determining the slope and y-intercept for graphing. The instructor emphasizes the importance of shading the correct region. The second inequality is solved similarly, with attention to flipping the inequality sign when dividing by a negative. The solution is the overlapping shaded region of both graphs.

What is the first step in preparing the inequality x + 2y > -6 for graphing?

• Divide both sides by 2

• Subtract x from both sides

• Add x to both sides

• Multiply both sides by 2

After rearranging the inequality x + 2y > -6, what is the slope of the line?

• -1/2

• 1/2

• 2

• -2

What type of line is used to graph the inequality y > -1/2x - 3?

• Dashed line

• Solid line

• Dotted line

• Thick line

What is the first step in preparing the inequality x - 2y < 2 for graphing?

• Add x to both sides

• Subtract x from both sides

• Multiply both sides by 2

• Divide both sides by 2

What happens to the inequality symbol when dividing by a negative number?

• It stays the same

• It disappears

• It becomes an equal sign

• It flips direction

What is the slope of the line for the inequality y < 1/2x - 1?

• -2

• 1/2

• 2

• -1/2

What type of line is used to graph the inequality y < 1/2x - 1?

• Thick line

• Solid line

• Dotted line

• Dashed line

Where should the shading be for the inequality y > -1/2x - 3?

• Below the line

• Above the line

• On the line

• No shading

Where should the shading be for the inequality y < 1/2x - 1?

• Above the line

• On the line

• No shading

• Below the line

What is the solution area for the system of inequalities?

• The area below both lines

• The area on the lines

• The area above both lines

• The area where the shading overlaps