Graphing Linear Inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

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

Back

The shaded area represents all the solutions to the inequality, indicating where the values of the variables satisfy the inequality.

Front

How do you determine if the shading is above or below the line in a linear inequality?

Back

If the inequality symbol is < or ≤, the shading is below the line. If it is > or ≥, the shading is above the line.

Front

What type of line is used for the inequality y < 3x - 2?

Back

A dashed line is used because the inequality does not include equality (i.e., it is not ≤ or ≥).

Front

What type of line is used for the inequality y ≥ -2x - 2?

Back

A solid line is used because the inequality includes equality (i.e., it is ≥).

Front

How do you graph the inequality y > 3x - 2?

Back

1. Graph the line y = 3x - 2 with a dashed line. 2. Shade the area above the line.

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 they are not included (> or <).

Front

How can you tell which inequality corresponds to a given graph?

Back

Identify the slope and y-intercept of the line, then determine the direction of shading to match it with the correct inequality.

Front

What does the inequality y < 4x - 2 indicate about the relationship between y and x?

Back

It indicates that for any value of x, y must be less than the value of 4x - 2.

Front

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

Back

The slope-intercept form is y = mx + b, where m is the slope and b is the y-intercept.