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 (e.g., <, >, ≤, ≥).

Front

What does the symbol '≥' indicate in an inequality?

Back

The symbol '≥' indicates that the value on the left is greater than or equal to the value on the right.

Front

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

Back

The symbol '≤' indicates that the value on the left is 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 solid or dashed line. 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 they are not included (> or <).

Front

What is the slope of a line?

Back

Front

How can you determine if a point is a solution to an inequality?

Back

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

Front

What does the inequality 'x < -1' represent on a number line?

Back

It represents all numbers to the left of -1, not including -1 itself.

Front

What is the solution set for the inequality 'y ≤ 5x - 1'?

Back

The solution set includes all points (x, y) that lie on or below the line represented by the equation y = 5x - 1.

Front

What is the significance of the equal sign in an inequality?

Back

The equal sign indicates that the boundary line is included in the solution set, resulting in a solid line.