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 (>, <, ≥, ≤). It represents a region of the coordinate plane.

Front

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

Back

The symbol '>' indicates that the values of the variable are greater than the value on the other side of the inequality.

Front

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

Back

The symbol '<' indicates that the values of the variable are less than the value on the other side of the inequality.

Front

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

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

Front

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

Back

The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

Front

How do you graph a linear inequality?

Back

To graph a linear inequality, first graph the corresponding linear equation as a dashed line (for < or >) or a solid line (for ≤ or ≥). Then shade the region that satisfies the inequality.

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, represented graphically as a shaded region on the coordinate plane.

Front

How can 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 coordinates of the point into the inequality. If the inequality holds true, the point is in the solution set.

Front

What is the difference between a strict inequality and a non-strict inequality?

Back

A strict inequality (>, <) does not include the boundary line, while a non-strict inequality (≥, ≤) includes the boundary line.

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.