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 (>, <, ≥, ≤).

Front

What does the symbol '≥' mean in an inequality?

Back

'≥' means 'greater than or equal to', indicating that the value can be either greater than or equal to the specified number.

Front

What type of line is used to represent '≥' or '≤' in a graph?

Back

A solid line is used to represent '≥' or '≤' because the boundary line is included in the solution set.

Front

What type of line is used to represent '>' or '<' in a graph?

Back

A dashed line is used to represent '>' or '<' because the boundary line is not included in the solution set.

Front

How do you determine if a point is a solution to a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does the solution set of a linear inequality represent?

Back

The solution set represents all the points (x, y) that satisfy the inequality.

Front

How can you graph the inequality y < 2x + 1?

Back

First, graph the line y = 2x + 1 with a dashed line, then shade below the line to represent all points where y is less than 2x + 1.

Front

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

Back

The boundary line separates the solution set from the non-solution set; whether it is solid or dashed indicates if points on the line are included.

Front

If the inequality is y ≥ -3/4 x + 3, what is the slope of the line?

Back

The slope of the line is -3/4.

Front

What does it mean if a point lies above the boundary line in a graph of an inequality?

Back

If a point lies above the boundary line, it is part of the solution set for inequalities of the form y > mx + b or y ≥ mx + b.