Graphing Linear Inequalities in Standard Form

The video tutorial covers graphing inequalities in standard form, focusing on solving for Y and graphing the resulting lines. It explains the process of moving terms, dividing by coefficients, and handling inequalities with greater than or less than signs. The tutorial also addresses the importance of dashed and solid lines based on inequality symbols and demonstrates how to shade the solution area. Special attention is given to flipping inequality signs when dividing by negative numbers.

What is the first step in solving for y in the inequality 4y + 2x = 8?

• Divide by 4

• Subtract 2x from both sides

• Multiply by 4

• Add 2x to both sides

After moving the x term in the inequality 4y > 2x + 8, what is the next step?

• Multiply by 4

• Divide by 4

• Subtract 2x from both sides

• Add 2x to both sides

When graphing the inequality y > -1/2x + 2, what type of line should be drawn?

• Bold line

• Dashed line

• Solid line

• Dotted line

In the inequality y < 2x + 3, what is the y-intercept?

• 2

• 3

• 1

• 0

What is the slope of the line y < 2x + 3?

• 2

• 3

• 1

• 1/2

When graphing y < 2x + 3, which direction should you shade?

• Below the line

• To the left of the line

• To the right of the line

• Above the line

What happens to the inequality sign when you divide by a negative number?

• It stays the same

• It flips

• It becomes an equal sign

• It disappears

In the inequality -4y ≥ 2x + 12, what is the result of dividing by -4?

• y ≤ -1/2x - 3

• y ≥ -1/2x - 3

• y ≤ 1/2x - 3

• y ≥ 1/2x - 3

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

• Dotted line

• Dashed line

• Bold line

• Solid line

When graphing y ≤ 1/2x - 3, which region should be shaded?

• Above the line

• Below the line

• To the left of the line

• To the right of the line