Graph and Identify Solutions of Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical expression that shows the relationship between two expressions using inequality symbols (>, <, ≥, ≤) 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, shade the region that satisfies the inequality (above the line for 'greater than' and below for 'less than').

Front

What does the shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the possible solutions (ordered pairs) that satisfy the inequality.

Front

What is the difference between a solid line and a dashed line in the graph of a linear inequality?

Back

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

Front

What is an ordered pair?

Back

An ordered pair is a pair of numbers used to represent a point on a coordinate plane, written in the form (x, y).

Front

How can you determine if an ordered pair is a solution to a linear inequality?

Back

To determine if an ordered pair is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the ordered pair is a solution.

Front

What does it mean for a point to be on the boundary line of a linear inequality?

Back

A point on the boundary line of a linear inequality is a potential solution; whether it is included in the solution set depends on whether the line is solid or dashed.

Front

What is the significance of the intercepts in the graph of a linear inequality?

Back

The intercepts (where the line crosses the axes) help to identify key points for graphing the inequality and understanding the feasible region.

Front

What is a feasible region in the context of linear inequalities?

Back

The feasible region is the area on the graph that satisfies all the constraints represented by the linear inequalities.

Front

How do you find the maximum or minimum value in a linear programming problem?

Back

To find the maximum or minimum value, evaluate the objective function at each vertex (corner point) of the feasible region.