Graphing linear inequalities

Front

What does a solid line represent in graphing linear inequalities?

Back

A solid line indicates that the points on the line are included in the solution set, which occurs when the inequality symbol is 'greater than or equal to' (≥) or 'less than or equal to' (≤).

Front

What does a dashed line represent in graphing linear inequalities?

Back

A dashed line indicates that the points on the line are not included in the solution set, which occurs when the inequality symbol is 'greater than' (>) or 'less than' (<).

Front

How can 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, then the point is a solution.

Front

What is the significance of shading in the graph of a linear inequality?

Back

Shading indicates the region of the graph that contains all the solutions to the inequality. The direction of shading depends on the inequality symbol.

Front

What is the first step in graphing a linear inequality?

Back

First, graph the corresponding linear equation as if it were an equality (using a solid or dashed line based on the inequality).

Front

What does the inequality y < 2x + 3 represent graphically?

Back

It represents all the points below the line y = 2x + 3, with a dashed line indicating that points on the line are not included.

Front

What is the difference between 'greater than' and 'greater than or equal to' in inequalities?

Back

'Greater than' (>) means the value is not included, while 'greater than or equal to' (≥) means the value is included.

Front

How do you test if a point lies in the solution set of a linear inequality?

Back

Substitute the coordinates of the point into the inequality. If the inequality is true, the point lies in the solution set.

Front

What is the general form of a linear inequality in two variables?

Back

The general form is Ax + By < C, Ax + By > C, Ax + By ≤ C, or Ax + By ≥ C, where A, B, and C are constants.

Front

What does the term 'boundary line' refer to in the context of linear inequalities?

Back

The boundary line is the line that represents the equation of the inequality. It separates the solution set from the non-solution set.