Graphing Linear Inequalities Explained

This lesson covers graphing systems of linear inequalities by focusing on rewriting inequalities in slope-intercept form, determining line types (solid or dashed), and using test points to decide shading. The instructor provides examples and practice problems to reinforce these concepts.

What is the primary difference in graphing systems of linear inequalities compared to linear equations?

• Looking for the point of intersection

• Determining where shading overlaps

• Using a different set of mathematical rules

• Graphing without using coordinates

When rewriting an inequality in slope-intercept form, what must you remember if you multiply or divide by a negative number?

• Subtract the constant term

• None of the above

• Flip the inequality symbol

• Multiply the slope by two

What does the slope-intercept form of a linear equation look like?

• b = mx + y

• y - b = mx

• mx - b = y

• y = mx + b

How do you determine the slope when rewriting an inequality for graphing?

• Divide the coefficient of x by the coefficient of y

• Multiply the x and y coefficients

• Subtract the y coefficient from the x coefficient

• Add the coefficients of x and y

Which type of line is used in a graph when the inequality includes an 'or equal to' condition?

• No line is drawn

• Solid line

• Dashed line

• Dotted line

In the context of graphing inequalities, what does a dashed line indicate?

• The inequality includes 'or equal to'

• The line represents an equation, not an inequality

• The inequality is strictly greater than or less than

• None of the above

What is the purpose of using a test point in graphing inequalities?

• To verify the equation of the line

• To establish the y-intercept

• To determine the correct shading area

• To find the slope of the line

If the test point (0,0) does not satisfy the inequality, where should you shade on the graph?

• Below the line

• No shading is required

• Above the line

• On the line

What should you do if the test point (0,0) is included in the solution of the inequality?

• Shade below the line

• Shade exactly on the line

• Shade above the line

• Do not shade at all

Why is it recommended to check your graph against the original inequality after graphing?

• To verify the shading is correct

• All of the above

• To ensure the slope was applied correctly

• To confirm no mistakes were made in rewriting the inequality