Graphing 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 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 symbol '≥' indicate in a linear inequality?

Back

The symbol '≥' indicates that the values of the variable are greater than or equal to the value on the other side of the inequality.

Front

What does the symbol '≤' indicate in a linear inequality?

Back

The symbol '≤' indicates that the values of the variable are less than or equal to the value on the other side of the inequality.

Front

What is the significance of the boundary line in graphing linear inequalities?

Back

The boundary line represents the values that make the inequality an equation. Depending on whether the line is solid or dashed, it indicates whether points on the line are included in the solution set.

Front

How do you determine which side of the boundary line to shade when graphing a linear inequality?

Back

To determine which side to shade, pick a test point not on the line (commonly (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the difference between strict and non-strict inequalities?

Back

Strict inequalities (<, >) do not include the boundary line, while non-strict inequalities (≤, ≥) include the boundary line in the solution set.

Front

What does the inequality 'y > 3x - 2' represent graphically?

Back

The inequality 'y > 3x - 2' represents the region above the line y = 3x - 2, excluding the line itself.

Front

How can you convert a linear inequality into slope-intercept form?

Back

To convert a linear inequality into slope-intercept form (y = mx + b), isolate y on one side of the inequality.

Front

What is the slope of the line represented by the inequality 'y ≤ 2/5x + 1'?

Back

The slope of the line represented by the inequality 'y ≤ 2/5x + 1' is 2/5.