Graphing Linear Inequalities on a Coordinate Plane

The video tutorial explains how to graph linear inequalities by converting them to slope-intercept form. It covers the process of graphing lines, determining whether they should be solid or dashed based on the inequality sign, and shading the appropriate region. Several examples are provided, including cases where the inequality sign flips, and special cases involving vertical and horizontal lines.

What form must a linear inequality be converted into for graphing?

• Quadratic form

• Slope-intercept form

• Point-slope form

• Standard form

What does a solid line in a graph of a linear inequality indicate?

• The inequality is strict (does not include the line)

• The inequality includes the line

• The inequality is only valid at the intercepts

• None of the above

How do you determine the direction to shade for a linear inequality?

• Use a test point to determine if it satisfies the inequality

• Always shade upwards

• Shade away from the origin

• Shade towards the y-intercept

What does a dashed line represent in the graph of a linear inequality?

• Inequality is only valid at the origin

• Inequality does not include the line

• Inequality is undefined

• Inequality includes the line

When graphing 'y > -1/3x - 2', why is the line solid?

• Because the inequality is strict

• Because the inequality includes equality

• Because the slope is negative

• None of the above

Why do we flip the inequality sign when dividing by a negative number?

• It's a standard rule without reason

• Because dividing by a negative reverses the inequality

• To adjust the y-intercept

• To correct the slope direction

In the inequality 'x < 2', why is the line vertical?

• Because it's a special rule for inequalities

• Because the slope is undefined

• Because the slope is zero

• Because it's an inequality in terms of x only

What direction do you shade for the inequality 'x < 2'?

• Shade above the line

• Shade to the left of the line

• Shade below the line

• Shade to the right of the line

For the inequality 'y >= -3', why is the line horizontal?

• Because the slope is zero

• Because y is isolated on one side

• Because the slope is undefined

• Because it's a special rule for y inequalities

Where do you shade for the inequality 'y >= -3'?

• Shade to the left of the line

• Shade above the line

• Shade to the right of the line

• Shade below the line