Flashcard 1: Linear Inequalities in Two Variables

Front

What does a solid line represent in a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol has 'or equal to' (≥ or ≤).

Front

What does a dashed line represent in a linear inequality?

Back

A dashed line indicates that the points on the line are NOT included in the solution set, which occurs when the inequality symbol is strictly greater than (>) or less than (<).

Front

How do you determine if a point is a solution to a linear inequality?

Back

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

Front

What is the general form of a linear inequality in two variables?

Back

The general form is Ax + By < C, Ax + By ≤ C, Ax + By > C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What are the four quadrants in a Cartesian plane?

Back

Quadrant I (x > 0, y > 0), Quadrant II (x < 0, y > 0), Quadrant III (x < 0, y < 0), Quadrant IV (x > 0, y < 0).

Front

How do you graph a linear inequality?

Back

1. Graph the boundary line (solid or dashed). 2. Choose a test point not on the line (usually (0,0)). 3. Determine which side of the line satisfies the inequality and shade that region.

Front

What is the solution set of a linear inequality?

Back

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

Front

What does the inequality 8x + 10y ≥ 162 represent in a real-world context?

Back

It represents a situation where the total seating capacity of circular and rectangular tables must be at least 162 guests.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line divides the Cartesian plane into two regions: one that satisfies the inequality and one that does not.

Front

How can you tell if a point lies on the boundary line of a linear inequality?

Back

A point lies on the boundary line if it satisfies the equation of the line derived from the inequality.