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 (>, <, ≥, ≤) instead of an equal sign.

Front

What does the symbol '≥' mean in a linear 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 a linear 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 above the line y = 3x - 2, not including the line itself.

Front

What does the inequality 'y ≤ 2/5x + 1' represent graphically?

Back

It represents the region below the line y = 2/5x + 1, including the line itself.

Front

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

Back

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

Front

What does the inequality 'x < -1' mean?

Back

It means that x can take any value less than -1, represented graphically by a dashed vertical line at x = -1, shading to the left.