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 such as <, >, ≤, or ≥.

Front

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

Back

The symbol '≤' means 'less than or equal to'. It indicates that the value on the left can be less than or equal to the value on the right.

Front

What does the symbol '≥' mean in a linear inequality?

Back

The symbol '≥' means 'greater than or equal to'. It indicates that the value on the left can be greater than or equal to the value on the right.

Front

How do you graph a linear inequality with '>' or '<'?

Back

Use a dashed line to represent the boundary line, indicating that points on the line are not included in the solution.

Front

How do you graph a linear inequality with '≥' or '≤'?

Back

Use a solid line to represent the boundary line, indicating that points on the line are included in the solution.

Front

What is the solution set of a linear inequality?

Back

The solution set of a linear inequality is the set of all points (x, y) that satisfy the inequality, often represented by shading a region on the graph.

Front

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

Back

Choose a test point not on the line (commonly (0,0)). If the point satisfies the inequality, shade the region containing that point; otherwise, shade the opposite region.

Front

What is the difference between 'y < mx + b' and 'y ≤ mx + b'?

Back

'y < mx + b' uses a dashed line and does not include points on the line, while 'y ≤ mx + b' uses a solid line and includes points on the line.

Front

What does the slope of a line in a linear inequality represent?

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises, while a negative slope means it falls.

Front

What is the y-intercept in the equation of a line?

Back

The y-intercept is the point where the line crosses the y-axis, represented by the value of y when x = 0.