Graphing Inequalities

Front

What is an inequality?

Back

An inequality is a mathematical statement that compares two expressions using symbols such as <, >, ≤, or ≥.

Front

What does the symbol '≥' mean?

Back

'≥' means 'greater than or equal to'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

How do you graph the inequality y > 2?

Back

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

Front

How do you graph the inequality y ≤ -3x + 1?

Back

Graph a solid line for y = -3x + 1 and shade the area below the line.

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 (≤ or ≥), while a dashed line indicates they are not included (< or >).

Front

What does it mean if a region is shaded above a line in a graph?

Back

It means that the solutions to the inequality are greater than the line's equation.

Front

What does it mean if a region is shaded below a line in a graph?

Back

It means that the solutions to the inequality are less than the line's equation.

Front

How do you determine the boundary line for the inequality y < -2x + 3?

Back

The boundary line is found by graphing the equation y = -2x + 3, using a dashed line since the inequality is '<'.

Front

What is the solution set for the inequality x ≥ -2?

Back

The solution set includes all values of x that are greater than or equal to -2.