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 '≤' 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

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

How do you graph a linear inequality with '>' or '<'?

Back

When graphing a linear inequality with '>' or '<', use a dashed line to indicate that points on the line are not included in the solution set.

Front

How do you graph a linear inequality with '≥' or '≤'?

Back

When graphing a linear inequality with '≥' or '≤', use a solid line to indicate that points on the line are included in 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

How do you determine if a point is in the solution set of a linear inequality?

Back

To determine if a point is in the solution set, substitute the x and y values of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

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

Back

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

Front

How do you convert a linear inequality to slope-intercept form?

Back

To convert a linear inequality to slope-intercept form, isolate y on one side of the inequality.

Front

What is the significance of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality by providing a starting point.