Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (>, <, ≥, ≤).

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the value on the left is either greater than or equal to the value on the right.

Front

What type of line is used to graph the inequality y > 3?

Back

A dashed line is used to graph y > 3, indicating that points on the line are not included in the solution set.

Front

How do you determine which side of the line to shade for the inequality y < 2?

Back

To determine which side to shade, pick a test point (like (0,0)). If it satisfies the inequality, shade the side containing that point.

Front

What does it mean if a point lies on the boundary line of a linear inequality?

Back

If a point lies on the boundary line of a linear inequality, it is included in the solution set if the line is solid (≥ or ≤) and not included if the line is dashed (> or <).

Front

What is the solution set of the inequality x < 4?

Back

The solution set includes all values of x that are less than 4, represented graphically by shading to the left of the vertical line x = 4.

Front

How do you graph the inequality y ≥ -2x + 1?

Back

Graph the line y = -2x + 1 as a solid line and shade above the line to represent all points where y is greater than or equal to the line.

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 they are not included (> or <).

Front

Which of the following points is a solution to the inequality y < 3? (0, 2), (1, 4), (2, 3)

Back

The point (0, 2) is a solution to the inequality y < 3.

Front

What does shading above a line indicate in a graph of an inequality?

Back

Shading above a line indicates that the solution set includes all points where the y-value is greater than the line.