Linear Inequalities & Systems of Linear Inequalities

Front

What is a linear inequality?

Back

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

Front

How do you graph a linear inequality in two variables?

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 solution set of a linear inequality represent?

Back

The solution set of a linear inequality represents all the ordered pairs (x, y) that make the inequality true.

Front

What is the difference between a solid line and a dashed line when 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

What is a system of linear inequalities?

Back

A system of linear inequalities consists of two or more linear inequalities that are considered simultaneously.

Front

How do you find the solution to a system of linear inequalities?

Back

To find the solution to a system of linear inequalities, graph each inequality on the same coordinate plane and identify the region where the shaded areas overlap.

Front

What does it mean for an ordered pair to be a solution of an inequality?

Back

An ordered pair (x, y) is a solution of an inequality if substituting x and y into the inequality makes the statement true.

Front

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

Back

To determine if a point is a solution, substitute the x and y values of the point into the inequality and check if the resulting statement is true.

Front

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

Back

The y-intercept is the point where the graph crosses the y-axis, and it helps in graphing the linear equation associated with the inequality.

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.