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

Front

How do you graph a linear inequality?

Back

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

Front

What does the solution of a linear inequality represent?

Back

The solution of a linear inequality represents all the points (x, y) that make the inequality true, forming a region in the coordinate plane.

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

Front

How do 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. If the inequality holds true, then the point is a solution.

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is typically written as Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What does the term 'feasible region' mean in the context of linear inequalities?

Back

The feasible region is the area on a graph where all the constraints (inequalities) overlap, representing all possible solutions to the system of inequalities.

Front

What is the significance of the boundary line in a linear inequality?

Back

The boundary line separates the coordinate plane into two regions: one that satisfies the inequality and one that does not. It is crucial for determining the feasible region.

Front

How can you solve a system of linear inequalities?

Back

To solve a system of linear inequalities, graph each inequality on the same coordinate plane and identify the overlapping shaded region, which represents the solution set.

Front

What is the role of the coefficients in a linear inequality?

Back

The coefficients in a linear inequality determine the slope and position of the boundary line, affecting the direction of the inequality and the feasible region.