Graphs of 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

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the values of the variable can be greater than or equal to a certain number.

Front

What does the symbol '≤' mean in a linear inequality?

Back

The symbol '≤' means 'less than or equal to'. It indicates that the values of the variable can be less than or equal to a certain number.

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

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does it mean if a point lies in the shaded region of a graph of a linear inequality?

Back

If a point lies in the shaded region, it means that the point satisfies the inequality and is a solution.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not.

Front

How can you tell which side of the boundary line to shade when graphing a linear inequality?

Back

You can test a point not on the line (like (0,0) if it's not on the line). If the point satisfies the inequality, shade the region containing that point.

Front

What is the solution set of a linear inequality?

Back

The solution set is the set of all points (x, y) that satisfy the inequality, represented graphically by the shaded region.