Graphing linear inequalities

Front

What is a linear inequality?

Back

A linear inequality is a mathematical statement that compares a linear expression to a value using inequality symbols (e.g., <, >, ≤, ≥).

Front

What does the graph of a linear inequality represent?

Back

The graph of a linear inequality represents all the solutions to the inequality, typically shaded to indicate the region that satisfies the inequality.

Front

What is the difference between a solid line and a dashed line in 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

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

Back

Substitute the coordinates of the point into the inequality. If the inequality holds true, the point is a solution.

Front

What does the inequality y ≥ -3/4 x + 3 mean in terms of graphing?

Back

It means that the region above the line y = -3/4 x + 3, including the line itself, is part of the solution set.

Front

What is the significance of the shading in the graph of a linear inequality?

Back

Shading indicates the set of all points that satisfy the inequality. The direction of shading depends on the inequality symbol.

Front

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

Back

1. Graph the line y = 2x + 3 with a dashed line. 2. Shade below the line to indicate that y values less than the line are included.

Front

What does it mean if a point lies on the dashed line of an inequality?

Back

If a point lies on a dashed line, it is not included in the solution set of the inequality.

Front

What is the first step in graphing a linear inequality?

Back

The first step is to graph the corresponding linear equation as if it were an equality.

Front

What is the role of the slope in graphing linear inequalities?

Back

The slope determines the steepness of the line and the direction of shading in the graph.