Graphing Linear Inequalities Concepts

This video tutorial covers graphing linear inequalities, building on the knowledge of graphing linear equations. It explains the differences between equations and inequalities, such as the use of dashed or solid lines depending on the inequality sign. The tutorial also demonstrates how to shade regions on the graph to represent solutions to inequalities, emphasizing the direction of shading based on whether the inequality is less than or greater than. Key learning points include understanding the inequality signs, line types, and shading techniques.

What is the main difference between graphing linear equations and linear inequalities?

• Linear equations use dashed lines.

• Linear inequalities use inequality signs.

• Linear equations have no slope.

• Linear inequalities do not use y-intercepts.

In the equation y = mx + b, what does 'm' represent?

• Constant

• Y-intercept

• Slope

• X-intercept

How do you plot the slope if it is -3?

• Up 3, right 1

• Down 3, right 1

• Up 3, left 1

• Down 3, left 1

What type of line is used for a 'less than' inequality without an equal sign?

• Solid line

• Dotted line

• Bold line

• Dashed line

What does a 'greater than' inequality indicate about the direction of shading?

• Shade below the line

• Shade above the line

• Shade to the right of the line

• Shade to the left of the line

When should you use a solid line in graphing inequalities?

• For all inequalities

• For 'greater than' inequalities

• For 'less than' inequalities

• For 'less than or equal to' and 'greater than or equal to' inequalities

What is the purpose of shading in graphing linear inequalities?

• To mark the y-intercept

• To show the slope

• To indicate the solution region

• To highlight the line

If an inequality is 'y < mx + b', where should you shade?

• To the right of the line

• Above the line

• Below the line

• To the left of the line

What should you do if the inequality sign has a line underneath it?

• Use a solid line

• Shade below the line

• Use a dashed line

• Shade above the line

What is the final step after graphing the line and shading the region?

• Erase the line

• Label the graph

• Change the slope

• Remove the shading