Graphing Linear Inequalities in Standard Form

This video tutorial covers graphing linear inequalities in standard form. It explains the differences between equations and inequalities, focusing on the use of boundary lines and shading to represent solution sets. The tutorial demonstrates how to find x and y intercepts, draw boundary lines, and verify solutions using test points. Several example problems are solved to illustrate these concepts, and the video concludes with a summary of the key steps and techniques for graphing linear inequalities.

What is the primary difference between a linear equation and a linear inequality in standard form?

• The presence of a variable

• The symbols used to connect terms

• The inequality or equality symbol

• The type of numbers used

When graphing a linear inequality, what does a solid boundary line indicate?

• The line is not part of the graph

• No solutions are included on the line

• The inequality is only greater than or less than

• The inequality includes equal to (≤ or ≥)

How do you find the x-intercept when graphing a linear inequality?

• Set y to zero and solve for x

• Set x to zero and solve for y

• Divide both sides by y

• Multiply both sides by x

What should you do if you divide by a negative number while solving an inequality?

• Multiply both sides by -1

• Add a negative sign to the result

• Reverse the direction of the inequality

• Subtract from both sides

In the inequality 3x - 4y > 12, if you cover the y-term, what inequality do you solve for x?

• 4y < 12

• 4y > 12

• 3x < 12

• 3x > 12

Which way should you shade the graph if the inequality symbol is 'less than'?

• Shade both sides

• Shade below the line

• Do not shade

• Shade above the line

What does a dashed line represent when graphing a linear inequality?

• The line represents multiple solutions

• The inequality does not include equal to

• The inequality includes equal to

• The line is not part of the solution

If the inequality is 'greater than', which direction should the graph be shaded?

• Do not shade

• Shade on the line only

• Shade upward

• Shade downward

What is the purpose of checking a point like (0,0) in the context of graphing inequalities?

• To calculate the x-intercept

• To find the y-intercept

• To verify the shaded area is correct

• To determine the slope of the line

What is the correct way to summarize the process of graphing a linear inequality?

• Shade the entire graph

• Only draw the line without shading

• Draw any line and shade randomly

• Find intercepts, draw the line, shade correctly, and check with a point