Graphing 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 graph of 'y < mx + b' represent?

Back

The region below the line y = mx + b, not including the line itself.

Front

What does the graph of 'y ≤ mx + b' represent?

Back

The region below the line y = mx + b, including the line itself.

Front

How do you determine if a point is a solution to a two-variable inequality?

Back

Substitute the x and y values of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What is the significance of the slope (m) in a two-variable inequality?

Back

The slope indicates the steepness of the line and the direction it goes (positive or negative) in the graph.

Front

What does the y-intercept (b) represent 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 = 0.

Front

What is the difference between '>' and '≥' in inequalities?

Back

'>' means the line is not included in the solution set, while '≥' means the line is included.

Front

How do you graph the inequality 'y > -4x - 1'?

Back

Graph the line y = -4x - 1 as a dashed line and shade the region above the line.

Front

What is the first step in graphing the inequality '2x - 3y < 12'?

Back

Rearrange the inequality to slope-intercept form (y = mx + b) to identify the slope and y-intercept.

Front

What does a dashed line indicate in graphing inequalities?

Back

A dashed line indicates that points on the line are not included in the solution set.