Linear Inequalities Flashcard

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

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.

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.

Front

What is the difference between '>' and '≥'?

Back

'>' means greater than, while '≥' means greater than or equal to.

Front

What is the significance of a dashed line in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set (used for < or >).

Front

What is the significance of a solid line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution set (used for ≤ or ≥).

Front

How do you determine if a point is in the solution set of an inequality?

Back

To determine if a point is in the solution set, substitute the point's coordinates into the inequality and check if the statement is true.

Front

What does the inequality y < 2/5x + 1 represent graphically?

Back

It represents the region below the line y = 2/5x + 1, not including the line itself.

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.

Front

How do you convert a linear equation to an inequality?

Back

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