Two Variable Inequalities

Front

What is a two-variable inequality?

Back

An inequality that involves two variables, typically written in the form of 'y < mx + b' or 'y > mx + b', where m is the slope and b is the y-intercept.

Front

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

Back

It means 'greater than'. For example, 'y > 3' indicates that y can take any value greater than 3.

Front

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

Back

It means 'less than'. For example, 'y < 5' indicates that y can take any value less than 5.

Front

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

Back

It means 'greater than or equal to'. For example, 'y ≥ 2' indicates that y can be 2 or any value greater than 2.

Front

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

Back

It means 'less than or equal to'. For example, 'y ≤ 4' indicates that y can be 4 or any value less than 4.

Front

How do you graph a two-variable inequality?

Back

1. Graph the corresponding equation as a line. 2. Use a solid line for '≥' or '≤' and a dashed line for '>' or '<'. 3. Shade the region that satisfies the inequality.

Front

What is the solution set of an inequality?

Back

The set of all ordered pairs (x, y) that make the inequality true.

Front

How can you determine if a point is a solution to an 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 the y-intercept in a two-variable inequality?

Back

The y-intercept is the point where the line crosses the y-axis, indicating the value of y when x is 0.

Front

What is the slope in a two-variable inequality?

Back

The slope (m) indicates the steepness of the line and the direction it goes. A positive slope rises from left to right, while a negative slope falls.