Inequalities and Their Conversions

The video tutorial explains how to convert inequalities from standard form to slope-intercept form. It provides multiple examples, demonstrating the process of rearranging terms and dividing by coefficients, while highlighting the importance of flipping the inequality sign when dividing by a negative number. The tutorial covers both positive and negative coefficients, ensuring a comprehensive understanding of the conversion process.

What is the first step in converting an inequality from standard form to slope-intercept form?

• Add the x-term to both sides

• Subtract the x-term from both sides

• Multiply both sides by the y-coefficient

• Divide both sides by the x-coefficient

In the inequality 3x + 4y ≥ 12, what is the result after subtracting 3x from both sides?

• 4y ≤ 3x + 12

• 4y ≤ -3x + 12

• 4y ≥ -3x + 12

• 4y ≥ 3x + 12

In the inequality 3x + 4y ≥ 12, what is the final form after conversion?

• y ≤ 3/4x + 3

• y ≤ -3/4x + 3

• y ≥ -3/4x + 3

• y ≥ 3/4x + 3

What is the y-intercept of the inequality 3x + 4y ≥ 12 after conversion?

• -4

• -3

• 3

• 4

What happens to the inequality symbol when you divide both sides by a negative number?

• It becomes an equal sign

• It disappears

• It flips direction

• It remains the same

After converting -5x - 2y < 1, what is the slope of the resulting inequality?

• -5/2

• 5/2

• -2/5

• 2/5

In the inequality -5x - 2y < 1, what is the final form after conversion?

• y > -5/2x - 5

• y < 5/2x - 5

• y < -5/2x - 5

• y > 5/2x - 5

What is the y-intercept of the inequality -5x - 2y < 1 after conversion?

• 5

• -5

• -2

• 2

In the inequality 2x - 3y ≤ -4, what is the first step to isolate y?

• Add 2x to both sides

• Multiply both sides by 3

• Divide both sides by 2

• Subtract 2x from both sides

What is the slope of the line after converting 2x - 3y ≤ -4 to slope-intercept form?

• 2/3

• -2/3

• 3/2

• -3/2