Homework Graphing Inequalities and Solutions

Front

What does it mean when a graph is shaded above the line?

Back

It indicates that the solutions to the inequality are all the points above the line, meaning the y-values are greater than the values on the line.

Front

What does it mean when a graph is shaded below the line?

Back

It indicates that the solutions to the inequality are all the points below the line, meaning the y-values are less than the values on the line.

Front

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

Back

A solid line indicates that the points on the line are included in the solution set (e.g., 'greater than or equal to'), while a dashed line indicates that the points on the line are not included (e.g., 'greater than').

Front

How do you determine the equation of a line from a graph?

Back

Front

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

Back

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

Front

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

Back

It means 'less than or equal to', indicating that the value can be either less than or exactly equal to the number.

Front

How can you tell if a point is part of the solution set for an inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, then the point is part of the solution set.

Front

What is the solution set of an inequality?

Back

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

Front

What does it mean if a point lies on the boundary line of an inequality?

Back

If the boundary line is solid, the point is included in the solution set. If the boundary line is dashed, the point is not included.

Front

Back

Draw a dashed horizontal line at y = 2 and shade the area above the line.