Graphing Inequalities: Key Concepts and Techniques

This video tutorial covers graphing linear inequalities, focusing on converting equations to slope-intercept form, plotting lines, and shading regions to represent solutions. It includes examples of graphing greater-than, less-than-or-equal-to, and vertical inequalities, emphasizing the importance of line types (dotted or solid) and shading directions. The tutorial also explains handling horizontal and vertical lines using the Hoy and Vux methods.

What is the first step in graphing a linear inequality?

• Plot the y-intercept

• Draw the line

• Convert the equation to slope-intercept form

• Identify the slope and intercept

What type of line is used when the inequality symbol is 'greater than' without an equal to?

• Solid line

• Dashed line

• Thick line

• Dotted line

When graphing 'y > mx + b', where should you shade?

• Below the line

• Above the line

• None of the above

• On the line

What does 'm = -2/1' indicate in the context of a linear equation?

• Vertical shift

• Horizontal shift

• Y-intercept

• Slope

In the inequality 'y <= mx + b', what type of line should be used?

• Dotted line

• None of the above

• Solid line

• Dashed line

When dividing by a negative number while solving for y, what must you remember to do with the inequality sign?

• Change the sign to equal

• Remove the sign

• Keep the sign the same

• Flip the sign

What does a 'Hoy' situation indicate in graphing inequalities?

• Vertical line

• Horizontal line

• Positive slope

• Negative slope

Where do you shade when the inequality is 'y < -4'?

• No shading needed

• On the line

• Below the line

• Above the line

What type of line is used for the inequality 'x > 7'?

• Dotted horizontal line

• Solid vertical line

• Dotted vertical line

• Solid horizontal line

In the context of 'x > 7', where should the shading be applied?

• Left of the line

• No shading is required

• Right of the line

• Directly on the line