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 solid line (for ≤ or ≥) or a dashed line (for < or >). Then, 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 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 boundary line in a linear inequality?

Back

The boundary line in a linear inequality separates the solution set from the non-solution set. Points on the line are included in the solution set if the inequality is ≤ 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 difference between a solid line and a dashed line in graphing linear 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 does the expression 'y ≤ 2/5x + 1' represent?

Back

The expression 'y ≤ 2/5x + 1' represents a linear inequality where the region below or on the line y = 2/5x + 1 is included in the solution set.

Front

How can you identify the solution region for the inequality '5x + y ≤ -1'?

Back

To identify the solution region for '5x + y ≤ -1', graph the line 5x + y = -1, use a solid line, and shade below the line.

Front

What does it mean if a point lies in the shaded area of a graph representing a linear inequality?

Back

If a point lies in the shaded area, it means that the point satisfies the inequality and is part of 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 and steepness of the line.