Exploring Systems of Linear Inequalities

This video tutorial provides an introduction to solving and graphing systems of linear inequalities. It covers the process of graphing inequalities in slope-intercept form, determining whether lines are solid or dashed, and identifying the regions to shade. The tutorial includes two examples, demonstrating how to graph and find the solution set for each system of inequalities.

What is the first step in solving and graphing systems of linear inequalities?

• Convert the inequalities to standard form.

• Identify the x-intercept.

• Convert the inequalities to slope-intercept form.

• Find the intersection points.

What is the slope of the inequality y ≥ (2/3)x + 1?

• 2/3

• 1

• 3

• 2

For the inequality y ≥ (2/3)x + 1, where do you start plotting the line?

• At the x-intercept

• At the y-intercept, which is 1

• At the slope

• At the origin

How do you determine if the line for an inequality should be solid or dashed?

• By the y-intercept

• By whether the inequality includes 'equal to'

• By the x-intercept

• By the slope

What is the slope of the inequality y < -x - 4?

• -1

• 1

• -4

• 4

For the inequality y < -x - 4, where do you start plotting the line?

• At the slope

• At the x-intercept

• At the y-intercept, which is -4

• At the origin

When combining the graphs of two inequalities, what determines the solution set?

• The intersection of the shaded regions

• The union of the shaded regions

• The area above both lines

• The area below both lines

What is the first step in graphing the inequality x + 2 > 0?

• Convert to slope-intercept form

• Identify the y-intercept

• Identify the x-intercept

• Recognize it as a vertical line

When dividing by a negative number in an inequality, what must you remember to do?

• Keep the inequality sign the same

• Add the same number to both sides

• Flip the inequality sign

• Subtract the same number from both sides

For the inequality -5x - 2y ≥ 6, what is the y-intercept after converting to slope-intercept form?

• 3

• -3

• 6

• -6