IP A.2H,A.3D Graphing & Writing 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 <, >, ≤, or ≥ c.

Front

What does the solution set of an inequality represent?

Back

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

Front

How do you graph a two-variable inequality?

Back

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

Front

What does the symbol '≤' mean in an inequality?

Back

It means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

What does the symbol '≥' mean in an inequality?

Back

It means 'greater than or equal to', indicating that the value can be either greater than or exactly equal to the number.

Front

How can you determine if a point is a solution to an inequality?

Back

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

Front

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

Back

The boundary line separates the solution set from the non-solution set; points on the line may or may not be included based on the inequality symbol.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than (not including the boundary), while '≥' means greater than or equal to (including the boundary).

Front

Write an inequality for the following situation: Aleris can spend no more than $24 on apples and oranges, where apples cost $3 each and oranges cost $2 each.

Back

3x + 2y ≤ 24, where x = number of apples and y = number of oranges.

Front

What does it mean if a point lies above the line in a graph of an inequality?

Back

It means that the point satisfies the inequality, indicating that the y-value is greater than the corresponding y-value on the line.