Two- Variable Inequalities

Front

What is a two-variable inequality?

Back

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

Front

What does the graph of a two-variable inequality represent?

Back

The graph represents all the solutions (ordered pairs) that satisfy 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 they are not included (> or <).

Front

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the solution set of an inequality?

Back

The set of all ordered pairs (x, y) that satisfy the inequality.

Front

What does it mean for a point to be on the boundary line of an inequality?

Back

It means that the point satisfies the equation of the boundary line, and whether it is included in the solution set depends on the type of inequality.

Front

How do you graph the inequality y ≥ 2x + 3?

Back

Graph the line y = 2x + 3 with a solid line, then shade above the line to represent all points where y is greater than or equal to 2x + 3.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means y increases as x increases, negative slope means y decreases as x increases).

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers (x, y) that represent a point on the Cartesian plane.

Front

How can you tell if a point is a solution to the inequality y < -x + 4?

Back

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