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 '≥' indicate in a linear inequality?

Back

'≥' means 'greater than or equal to', indicating that the values satisfying the inequality include the boundary line.

Front

What does the symbol '>' indicate in a linear inequality?

Back

'>' means 'greater than', indicating that the values satisfying the inequality do not include the boundary line.

Front

How do you determine if a line is solid or dashed in a graph of a linear inequality?

Back

Use a solid line for '≥' or '≤' (includes boundary) and a dashed line for '>' or '<' (excludes boundary).

Front

When graphing the inequality y ≥ -2x + 1, where do you shade?

Back

Shade above the line because the inequality indicates values greater than or equal to the line.

Front

What is the solution set of a linear inequality?

Back

The solution set includes all the points (x, y) that satisfy the inequality.

Front

How do you graph the inequality y < 4x - 2?

Back

Graph the line y = 4x - 2 as a dashed line and shade below it.

Front

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

Back

If the line is solid, the point is included in the solution set; if dashed, it is not included.

Front

What is the first step in graphing a linear inequality?

Back

Convert the inequality to slope-intercept form (y = mx + b) if necessary.

Front

How do you find the boundary line for the inequality y > 3x + 7?

Back

Graph the line y = 3x + 7 as a dashed line since the inequality is 'greater than'.