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 such as <, >, ≤, or ≥.

Front

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

Back

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

Front

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

Back

The symbol '≥' indicates that the value on the left is greater 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 line if the inequality includes '≤' or '≥', or as a dashed line if it includes '<' 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 set (for '≤' or '≥'), while a dashed line indicates that points on the line are not included (for '<' or '>').

Front

How can 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, then the point is part of the solution set.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality.

Front

What does it mean if a point is not part of the solution set?

Back

It means that when the coordinates of that point are substituted into the inequality, the inequality does not hold true.

Front

How do you identify the boundary line of a linear inequality?

Back

The boundary line is identified by rewriting the inequality as an equation (e.g., y = mx + b) and graphing it. The type of line (solid or dashed) depends on the inequality symbol.

Front

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

Back

The slope-intercept form is given by the equation y = mx + b, where m is the slope and b is the y-intercept.