Two-Variable Inequalities

Front

What is a two-variable inequality?

Back

Front

What does it mean to graph a two-variable inequality?

Back

Graphing a two-variable inequality involves representing the solutions of the inequality on a coordinate plane, typically using a boundary line and shading the appropriate region.

Front

What is the significance of the boundary line in graphing inequalities?

Back

The boundary line represents the points where the inequality becomes an equation. If the inequality is strict (e.g., < or >), the line is dashed; if it is inclusive (e.g., \leq or \geq), the line is solid.

Front

When do you use a dashed line when graphing inequalities?

Back

Front

When do you use a solid line when graphing inequalities?

Back

Front

What does shading above the line indicate in graphing inequalities?

Back

Front

What does shading below the line indicate in graphing inequalities?

Back

Front

How do you determine if a point is a solution to a two-variable inequality?

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the solution set of a two-variable inequality?

Back

The solution set of a two-variable inequality is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region on the graph.

Front

What is the difference between a strict and non-strict inequality?

Back

A strict inequality (e.g., < or >) does not include the boundary line, while a non-strict inequality (e.g., \leq or \geq) includes the boundary line.