Izzy - Graphing Inequalities in Two Variables

Front

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

Back

The general form of a linear inequality in two variables is Ax + By <, >, ≤, or ≥ C, where A, B, and C are constants.

Front

How do you graph a linear inequality in two variables?

Back

To graph a linear inequality, first graph the corresponding linear equation as a boundary line. Then, use a dashed line for < or > and a solid line for ≤ or ≥. Finally, shade the appropriate region based on the inequality.

Front

What does the shaded region in the graph of a linear inequality represent?

Back

The shaded region represents all the solutions to the inequality, indicating where the inequality holds true.

Front

How can you determine if a point is a solution to a linear inequality?

Back

To determine if a point is a solution, substitute the x and y coordinates of the point into the inequality. If the inequality holds true, then the point is a solution.

Front

What is the difference between a solid line and a dashed line when graphing inequalities?

Back

A solid line indicates that points on the line are included in the solution (≤ or ≥), while a dashed line indicates that points on the line are not included ( < or > ).

Front

What does the inequality y > 3/4x + 5 represent graphically?

Back

The inequality y > 3/4x + 5 represents the region above the line y = 3/4x + 5, where all points (x, y) satisfy the inequality.

Front

What is the significance of the slope in a linear inequality?

Back

The slope indicates the steepness of the line and the direction of the inequality. A positive slope means the line rises from left to right, while a negative slope means it falls.

Front

How do you identify the correct graph for a given inequality?

Back

To identify the correct graph, look for the boundary line corresponding to the inequality and check which side of the line is shaded to represent the solution set.

Front

What does the inequality y ≤ -x + 2 indicate about the graph?

Back

The inequality y ≤ -x + 2 indicates that the region below and including the line y = -x + 2 is part of the solution set.

Front

What is the role of the y-intercept in graphing linear inequalities?

Back

The y-intercept is the point where the line crosses the y-axis and helps in plotting the line accurately on the graph.