Graphing Linear Inequalities

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 ≥). It represents a region of the coordinate plane.

Front

How do you graph a linear inequality?

Back

1. Start by graphing the corresponding linear equation as a solid line (for ≤ or ≥) or a dashed line (for < or >). 2. Choose a test point not on the line to determine which side of the line to shade. 3. Shade the region that satisfies the inequality.

Front

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

Back

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

Front

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

Back

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

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (for ≤ or ≥), while a dashed line indicates that points on the line are not included (for < or >).

Front

How do you determine the solution set of a linear inequality?

Back

The solution set of a linear inequality consists of all the points in the shaded region of the graph, which satisfy the inequality.

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you convert a linear inequality to slope-intercept form?

Back

Front

What is the significance of the y-intercept in a linear inequality?

Back

The y-intercept is the point where the line crosses the y-axis. It helps in graphing the inequality and understanding the relationship between the variables.

Front

How can you check if a point is a solution to a linear inequality?

Back

To check if a point (x, y) is a solution, substitute the x and y values into the inequality. If the inequality holds true, then the point is a solution.