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 shaded region in a graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

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

Back

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

Front

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

Back

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

Front

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

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of the slope in the equation of a line?

Back

The slope indicates the steepness of the line and the direction it goes (positive slope rises, negative slope falls).

Front

What does the y-intercept represent in the equation of a line?

Back

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

Front

How do you graph a linear inequality?

Back

1. Graph the corresponding linear equation. 2. Use a solid or dotted line based on the inequality. 3. Shade the appropriate region based on the inequality.

Front

What is the difference between 'y > mx + b' and 'y ≥ mx + b'?

Back

'y > mx + b' uses a dotted 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 inequality 'x ≤ 12' mean in a real-world context?

Back

It means that a person must be 12 years old or younger to qualify for something, such as ordering from a kids menu.