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'. It indicates that the value on the left is either greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left is either less than or equal to the value on the right.

Front

How do you graph a linear inequality?

Back

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

Front

What is the difference between a dashed line and a solid line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution (for < or >), while a solid line indicates that points on the line are included (for ≤ or ≥).

Front

What does the inequality 'y < 3x - 2' represent graphically?

Back

It represents the region below the line y = 3x - 2, not including the line itself.

Front

What is the solution set of the inequality 'y ≥ 2'?

Back

The solution set includes all points on or above the horizontal line y = 2.

Front

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

Back

Choose a test point not on the line (commonly (0,0)). Substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

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 does the slope of a line indicate in the context of inequalities?

Back

The slope indicates the steepness of the line and the direction of the inequality (positive slope means the line rises, negative slope means it falls).