Two- Variable Inequalities

Front

What is a two-variable inequality?

Back

A two-variable inequality is a mathematical statement that compares two expressions involving two variables, typically written in the form of 'ax + by <, >, ≤, or ≥ c'.

Front

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

Back

The solution set of a two-variable inequality represents all the points (x, y) in the coordinate plane that satisfy the inequality.

Front

How do you graph a two-variable inequality?

Back

To graph a two-variable inequality, first graph the corresponding equation as a line, then use a dashed line for < or > and a solid line for ≤ or ≥. 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 (≤ or ≥), while a dashed line indicates that points on the line are not included (< or >).

Front

How can you determine if a point is part of the solution set for a two-variable inequality?

Back

To determine if a point is part of the solution set, substitute the coordinates of the point into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What does the inequality y ≤ -3/4 x + 3 represent graphically?

Back

The inequality y ≤ -3/4 x + 3 represents the region below the line y = -3/4 x + 3, including the line itself.

Front

What is the significance of the slope in a two-variable inequality?

Back

The slope in a two-variable inequality indicates the steepness and direction of the line. A positive slope means the line rises, while a negative slope means it falls.

Front

What does the expression |x + 3| represent in an inequality?

Back

The expression |x + 3| represents the absolute value of (x + 3), which is the distance of (x + 3) from zero on the number line.

Front

How do you solve a two-variable inequality?

Back

To solve a two-variable inequality, isolate one variable on one side of the inequality and then graph the resulting inequality.

Front

What is the meaning of the inequality y > |x - 3| + 2?

Back

The inequality y > |x - 3| + 2 represents the region above the graph of the function y = |x - 3| + 2.