Graphing Inequalities Concepts

This video tutorial covers graphing linear inequalities, starting with an introduction to the concept and moving through solving inequalities with ordered pairs. It explains how to graph inequalities using slope-intercept form, discusses shading and line types, and demonstrates using graphing calculators. The tutorial concludes with writing inequalities from graphed regions.

What is the main difference between graphing inequalities on a number line and on a coordinate plane?

• Number lines are used for graphing equations, not inequalities.

• Coordinate planes require a pair of numbers for each point.

• Coordinate planes can only represent one variable.

• Number lines can represent two variables.

How do you determine if an ordered pair is a solution to an inequality?

• By checking if the pair lies on the line.

• By substituting the pair into the inequality.

• By graphing the pair on a number line.

• By comparing the pair to the y-intercept.

What form should an inequality be in to graph it using slope-intercept form?

• Quadratic form

• Slope-intercept form

• Point-slope form

• Standard form

What does a solid line indicate when graphing an inequality?

• The inequality includes the equal to condition.

• The inequality is quadratic.

• The points on the line are not solutions.

• The inequality is strict (no equal to).

Why is it important to use test points when graphing inequalities?

• To check if the line is solid or dotted.

• To decide which side of the line to shade.

• To find the y-intercept.

• To determine the slope of the line.

What should you do if a test point does not satisfy the inequality?

• Shade the opposite side of the line from the test point.

• Shade the side of the line where the test point lies.

• Change the inequality to an equation.

• Use a different test point on the same side.

How can a graphing calculator assist in graphing inequalities?

• It can only graph equations, not inequalities.

• It automatically shades the correct region.

• It provides the exact coordinates of the intercepts.

• It converts inequalities to equations.

What is the significance of the shaded region in a graph of an inequality?

• It highlights the y-intercept.

• It represents the solutions to the inequality.

• It shows the area where the inequality is not valid.

• It indicates the slope of the line.

When writing an inequality for a shaded region, what is the first step?

• Choose a test point.

• Determine the slope of the line.

• Identify the y-intercept.

• Write the equation of the line.

What happens if you change the direction of the inequality sign when graphing?

• The y-intercept is altered.

• The slope of the line changes.

• The shaded region switches sides.

• The line becomes dotted.