Two-Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically written in the form of 'ax + by < c', 'ax + by > c', etc.

Front

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

Back

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

Front

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

Back

Substitute the point's coordinates into the inequality. If the inequality holds true, the point is part of the solution set.

Front

What is the graphical representation of a two-variable inequality?

Back

A region on the coordinate plane, often bounded by a line, where one side of the line represents the solution set.

Front

What does a dashed line indicate in the graph of an inequality?

Back

It indicates that points on the line are not included in the solution set (for < or > inequalities).

Front

What does a solid line indicate in the graph of an inequality?

Back

It indicates that points on the line are included in the solution set (for ≤ or ≥ inequalities).

Front

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

Back

Graph the line y = 2x + 3 with a dashed line, then shade below the line.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and does not include the line in the solution, while 'y ≤ mx + b' uses a solid line and includes the line.

Front

What does the term 'boundary line' refer to in the context of inequalities?

Back

The line that separates the solution set from the non-solution set in a graph of a two-variable inequality.

Front

How can you identify the correct graph for a given inequality?

Back

By analyzing the slope and y-intercept of the line, and determining the correct shading direction based on the inequality sign.