Exploring Systems of Inequalities

Why is it important to rearrange an inequality to the form y = mx + b before graphing?

• It allows for easier identification of the slope and y-intercept.

• It makes it easier to find the x-intercept.

• It simplifies the inequality.

• It helps in solving the inequality algebraically.

What is the first step in graphing the inequality y - 3x > 2?

• Shading the region.

• Drawing the line.

• Plotting the points.

• Solving for y.

When graphing y - 3x > 2, where do you start on the graph?

• At the x-intercept.

• At the point (3, 2).

• At the y-intercept, which is 2.

• At the origin.

What type of line is used to graph y - 3x > 2?

• Dashed line.

• Solid line.

• Dotted line.

• Curved line.

For the inequality 3y ≤ -2x - 6, what is the first step to isolate y?

• Add 2x to both sides.

• Subtract 2x from both sides.

• Multiply everything by 3.

• Divide everything by 3.

How do you determine the shading for the inequality 3y ≤ -2x - 6?

• Shade above the line.

• Shade below the line.

• Shade to the left of the line.

• Shade to the right of the line.

What is the significance of the overlapping region when graphing systems of inequalities?

• It represents the solution to the system.

• It shows where the lines intersect.

• It highlights the y-intercepts.

• It indicates the x-intercepts.

When graphing y < 12x + 5, what type of line should be used?

• Dashed line.

• Dotted line.

• Solid line.

• Curved line.

For the inequality 3y ≥ -5x + 9, what happens to the inequality symbol when dividing by a negative number?

• It disappears.

• It becomes an equal sign.

• It flips direction.

• It stays the same.

In the final example, what is the solution region for the system of inequalities?

• The region above both lines.

• The region below both lines.

• The region where the shading overlaps.

• The region where the lines intersect.