Graphing Inequalities in Two Variables

This video tutorial covers graphing inequalities with two variables, focusing on how to graph inequalities like Y ≥ 2, X < -1, X < Y, X ≤ 2Y, X + Y > 1, and X - Y > 1. It explains the process of converting inequalities into lines, using solid or dashed lines based on the inequality type, and shading the appropriate regions to represent solutions. The tutorial emphasizes understanding the relationship between the inequality and the graph, ensuring students can visualize and solve inequalities graphically.

What is the first step in graphing an inequality?

• Shade the region immediately.

• Pretend the inequality is a line.

• Start with plotting points.

• Draw a dashed line regardless of the inequality.

When graphing 'Y > 2', how do you represent the inequality on the graph?

• By drawing a vertical line through Y = 2.

• By shading below the line Y = 2.

• By drawing a dashed line only.

• By shading above the line Y = 2.

How do you graph 'X < -1' on the XY plane?

• By shading to the right of X = -1.

• By shading above the line X = -1.

• By shading to the left of X = -1.

• By drawing a solid line through X = -1.

What does a dashed line indicate when graphing inequalities?

• The inequality includes the line.

• The inequality cannot be graphed.

• The inequality is only valid at one point.

• The inequality does not include the line.

When graphing 'Y = X', which direction do you shade if the inequality is 'Y > X'?

• Shade to the right of the line.

• Shade above the line.

• Shade below the line.

• No shading is needed.

In graphing inequalities, what does shading represent?

• The solution set of the inequality.

• The exact points of the inequality.

• The maximum value of the inequality.

• The area where the inequality is not true.

How is a 'greater than or equal to' inequality represented on a graph?

• With a dashed line and shading above.

• With a solid line and shading above.

• With a dashed line and no shading.

• With a solid line and shading below.

What does a solid line in an inequality graph signify?

• The inequality is only true for the values on the line.

• The inequality includes the values on the line.

• The inequality does not include the values on the line.

• The line represents an equation, not an inequality.

What change occurs to the inequality sign when dividing both sides by a negative number?

• The sign remains the same.

• The sign flips.

• The inequality becomes an equation.

• The inequality is no longer valid.

When graphing 'X - Y > 1', in which direction is the shading applied?

• Shading is applied above the line.

• Shading is applied to the right of the line.

• Shading is applied below the line.

• No shading is applied; only a dashed line is drawn.