Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation as a solid line (for ≥ or ≤) or a dashed line (for > or <). 2. Shade the region that satisfies the inequality.

Front

What does the dashed line represent in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set (for inequalities using < or >).

Front

What does the solid line represent in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution set (for inequalities using ≤ or ≥).

Front

How do you determine which side of the line to shade for an inequality?

Back

Choose a test point not on the line (commonly (0,0)). If the inequality is true for that point, shade the region containing the point; otherwise, shade the opposite side.

Front

What is the inequality symbol for 'greater than'?

Back

>

Front

What is the inequality symbol for 'less than or equal to'?

Back

≤

Front

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

Back

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

Front

How do you find the slope of a line from an equation?

Back

In the slope-intercept form (y = mx + b), the slope is the coefficient of x (m).

Front

What does the y-intercept represent in a graph?

Back

The y-intercept is the point where the line crosses the y-axis (where x = 0).