Graphing a System of Linear Inequalities

Front

What does the graph of y ≥ x - 3 represent?

Back

The area above or on the line y = x - 3 is shaded, indicating all points (x, y) that satisfy the inequality.

Front

Which points are part of the solution set for the inequality y < 2x + 1?

Back

Any point (x, y) that lies below the line y = 2x + 1.

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 they are not included (> or <).

Front

How do you determine if a point is a solution to a system of inequalities?

Back

Substitute the point's coordinates into each inequality. If the point satisfies all inequalities, it is part of the solution set.

Front

What is the solution set of a system of linear inequalities?

Back

The solution set is the region where the shaded areas of all inequalities overlap on the graph.

Front

What does the inequality y < 3 represent on a graph?

Back

It represents the area below the horizontal line y = 3.

Front

How do you graph the inequality y ≥ 2x - 4?

Back

Graph the line y = 2x - 4 with a solid line and shade above the line.

Front

What is the significance of the intersection of two inequalities on a graph?

Back

The intersection represents the set of points that satisfy both inequalities.

Front

Which symbol indicates that a point on the line is included in the solution?

Back

The symbols ≤ and ≥ indicate that points on the line are included.

Front

What is the first step in graphing a system of linear inequalities?

Back

Graph each inequality as if it were an equation to find the boundary lines.