Graphing Systems of Inequalities

Mrs. Fallcheck explains how to graph systems of inequalities, focusing on shading regions and identifying solution sets. The tutorial covers graphing individual inequalities, determining line types, and using a calculator for graphing. Key points include understanding inequality symbols, shading directions, and identifying solution regions where shaded areas overlap.

What is the main focus when graphing systems of inequalities?

• Shading regions and finding where they overlap

• Identifying the slope and y-intercept

• Calculating the exact values of x and y

• Finding the intersection point of two lines

What type of line is used for the inequality y > -2x - 9?

• Solid line

• Dashed line

• Dotted line

• Bold line

When graphing y ≤ -2x - 9, where should you shade?

• To the right of the line

• To the left of the line

• Below the line

• Above the line

What does a dashed line indicate in the context of graphing inequalities?

• Only the x-intercept is included in the solution

• All points on the line are included in the solution

• No points on the line are included in the solution

• Only the y-intercept is included in the solution

In the example, why is the point (-8, 7) not a solution?

• It is not on any line

• It is on a dashed line

• It is on a solid line

• It lies outside the shaded region

What is the first step in graphing the inequality y < -5?

• Shade below the line

• Draw a vertical line at x = -5

• Draw a horizontal line at y = -5

• Shade above the line

How do you graph the inequality -2y ≥ x - 14 using a calculator?

• Divide both sides by -2 and then enter it

• Enter the equation as it is

• Multiply both sides by -2 and then enter it

• Subtract 14 from both sides and then enter it

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

• It disappears

• It flips direction

• It remains the same

• It becomes an equal sign

What is the y-intercept of the line y = -1/2x + 7?

• 1/2

• -7

• -1/2

• 7

Where is the solution region for the system of inequalities y < -5 and -2y ≥ x - 14?

• Where the shaded regions overlap

• Where the lines intersect

• Below both lines

• Above both lines