Two- Variable Inequalities

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that relates two variables using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign. It represents a region of the coordinate plane.

Front

What does the solution set of a two-variable inequality represent?

Back

The solution set of a two-variable inequality represents all the ordered pairs (x, y) that satisfy the inequality, forming a region on the graph.

Front

How do you graph a two-variable inequality?

Back

1. Graph the corresponding equation as if it were an equality. 2. Use a solid line for ≤ or ≥ and a dashed line for < or >. 3. Shade the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What does the inequality @@y ge -2(x-3)^2 + 2@@ represent?

Back

Front

What is the significance of the vertex in a quadratic inequality?

Back

The vertex of a quadratic inequality is the highest or lowest point of the parabola, which helps determine the direction of the shading in the graph.

Front

What does it mean for a point to be 'not part of the solution set'?

Back

It means that when the coordinates of the point are substituted into the inequality, the inequality does not hold true.

Front

How do you identify the correct inequality from a graph?

Back

Look at the direction of the shading and the type of line used (solid or dashed) to determine the correct inequality symbol.

Front

What is the general form of a linear inequality in two variables?

Back