Writing Linear Inequalities from Graphs

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

How do you represent a linear inequality graphically?

Back

A linear inequality is represented graphically by a shaded region on one side of a boundary line, which represents the solutions to the inequality.

Front

What does a dashed line indicate in the graph of a linear inequality?

Back

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

Front

What does a solid line indicate in the graph of a linear inequality?

Back

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

Front

How do you determine which side of the line to shade in a linear inequality?

Back

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

Front

What is the standard form of a linear inequality?

Back

The standard form of a linear inequality is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What is the difference between '>' and '≥' in linear inequalities?

Back

'>' means that the value is strictly greater than, while '≥' means that the value is greater than or equal to.

Front

What is the difference between '<' and '≤' in linear inequalities?

Back

'<' means that the value is strictly less than, while '≤' means that the value is less than or equal to.

Front

How can you convert a word problem into a linear inequality?

Back

Identify the quantities involved, determine the relationship between them, and express it using inequality symbols based on the context of the problem.

Front

What is a boundary line in the context of linear inequalities?

Back

A boundary line is the line that represents the equation of the linear inequality, separating the solution set from non-solution set.