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 ≥.

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 symbol '>' indicate in a linear inequality?

Back

The symbol '>' indicates that the values of the variable are greater than 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 the value on the other side of the inequality.

Front

What is the difference between a solid line and a dashed line when graphing linear inequalities?

Back

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

Front

How do you determine which side of the 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 graphical representation of the inequality y < 3?

Back

The graphical representation of the inequality y < 3 is a dashed horizontal line at y = 3, with the area below the line shaded.

Front

What does the inequality y ≥ (1/3)x - 5 represent graphically?

Back

The inequality y ≥ (1/3)x - 5 represents a solid line with a slope of 1/3 and a y-intercept of -5, with the area above the line shaded.

Front

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

Back

The slope-intercept form of a linear equation is given by y = mx + b, where m is the slope and b is the y-intercept.

Front

How can you convert a linear equation into a linear inequality?

Back

To convert a linear equation into a linear inequality, replace the equality sign (=) with an inequality sign (<, >, ≤, or ≥).