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 'greater than'.

Front

What does the symbol '≤' mean?

Back

'≤' means 'less than or equal to'.

Front

What does the symbol '<' mean?

Back

'<' means 'less than'.

Front

How do you graph the inequality y < -1/2x + 3?

Back

1. Graph the line y = -1/2x + 3 as a dashed line. 2. Shade below the line to represent y values less than 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 (≥ or ≤), while a dashed line indicates they are not included (> or <).

Front

How do you determine which side of the line to shade when graphing an inequality?

Back

Choose a test point not on the line (usually (0,0) if it's not on the line) and substitute it into the inequality. If the inequality holds true, shade the side containing the test point.

Front

What is the graph of y ≥ -3?

Back

A solid horizontal line at y = -3, with shading above the line.

Front

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

Back

1. Graph the line y = -x + 1 as a solid line. 2. Shade below the line to represent y values less than or equal to the line.