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

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a dashed or solid line. 2. Determine which side of the line to shade based on the inequality symbol.

Front

What does it mean if a line is dashed in a graph of a linear inequality?

Back

A dashed line indicates that the points on the line are not included in the solution set (i.e., the inequality is strict: > or <).

Front

What does it mean if a line is solid in a graph of a linear inequality?

Back

A solid line indicates that the points on the line are included in the solution set (i.e., the inequality is non-strict: ≥ or ≤).

Front

How do you determine which side of the line to shade for the inequality y > mx + b?

Back

Shade above the line if the inequality is 'greater than' (>) and below the line if it is 'less than' (<).

Front

What is the slope-intercept form of a linear equation?

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis, and it helps in graphing the inequality.

Front

How can you convert a linear inequality into slope-intercept form?

Back

Isolate y on one side of the inequality to express it in the form y < mx + b or y > mx + b.

Front

What does the term 'rise over run' refer to in graphing?

Back

'Rise over run' refers to the slope of a line, calculated as the change in y (rise) divided by the change in x (run).

Front

What is the equivalent inequality for 3x - y > 4?

Back

y < 3x - 4.