Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that relates a linear expression to a value using inequality symbols (such as <, >, ≤, or ≥) instead of an equal sign.

Front

How do you graph a linear inequality?

Back

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

Front

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

Back

The symbol '≤' means 'less than or equal to', indicating that the values of the variable can be less than or equal to a certain number.

Front

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

Back

The symbol '≥' means 'greater than or equal to', indicating that the values of the variable can be greater than or equal to a certain number.

Front

What is the difference between a dashed line and a solid line in graphing inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution (for < or >), while a solid line indicates that the points on the line are included in the solution (for ≤ or ≥).

Front

How do you determine which side of the line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

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

Back

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

Front

How can you convert a linear equation into an inequality?

Back

To convert a linear equation into an inequality, replace the equal sign with an inequality symbol (such as <, >, ≤, or ≥) based on the context of the problem.

Front

What does the solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the points (x, y) that satisfy the inequality, which can be visualized as a shaded region on a graph.

Front

What is the significance of the y-intercept in a linear inequality?

Back

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