Practice Graphing Two Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically written in the form ax + by < c, ax + by > c, ax + by ≤ c, or ax + by ≥ c.

Front

How do you graph a two-variable inequality?

Back

1. Graph the boundary line (as a solid line for ≤ or ≥, dashed for < or >). 2. Choose a test point not on the line to determine which side of the line to shade.

Front

What does it mean if a point is on the boundary line of a graph 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 (≤ or ≥ includes it, < or > does not).

Front

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

Back

The set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on the coordinate plane.

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 do you write an inequality from a word problem?

Back

Identify the quantities involved, determine the relationship (greater than, less than, etc.), and express it using variables and an inequality symbol.

Front

What does the inequality 3x + 2y ≤ 24 represent in a word problem context?

Back

It represents a situation where the total cost of apples (3x) and oranges (2y) cannot exceed $24.

Front

What is a test point in graphing inequalities?

Back

A point used to determine which side of the boundary line to shade; if the point satisfies the inequality, that side is shaded.

Front

What does it mean for an inequality to be 'at least' a certain value?

Back

It means the value must be greater than or equal to that number, represented by the symbol ≥.

Front

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

Back

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