Linear Inequalities in Two Variables

Front

What is a linear inequality in two variables?

Back

Front

What does the symbol < mean in a linear inequality?

Back

The symbol < indicates that the line is dashed, meaning points on the line are not included in the solution set.

Front

What does the symbol \leq mean in a linear inequality?

Back

The symbol \leq indicates that the line is solid, meaning points on the line are included in the solution set.

Front

How do you determine which side of the line to shade in a linear inequality?

Back

To determine which side to shade, you can test a point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the side containing that point.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, represented graphically as a shaded region on a 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 (for inequalities with \leq or \geq), while a dashed line indicates that points on the line are not included (for inequalities with < or >).

Front

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

Back

1. Graph the line y = 2x + 3 as a dashed line. 2. Shade the area below the line to represent all points where y is less than 2x + 3.

Front

Which of the following points is NOT part of the solution set for the inequality y < 2x + 3: (0, 0), (5, 1), (-1, -3), (20, -5)?

Back

The point (-1, -3) is NOT part of the solution set.

Front

What does the inequality x > -2 represent graphically?

Back

The inequality x > -2 represents a vertical dashed line at x = -2, with shading to the right of the line.

Front

What does the inequality y \leq -1 represent graphically?

Back

The inequality y \leq -1 represents a horizontal solid line at y = -1, with shading below the line.