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An inequality is a mathematical statement that explains the relative size of two expressions. It shows that one value is less than, greater than, less than or equal to, or greater than or equal to another value.

The inequality sign '<' means 'less than', indicating that the value on the left is smaller than the one on the right. Conversely, the '>' sign denotes 'greater than'.

In the exercise, we have the inequality \( y < 0 \). This means that we are looking for values of \( y \) that are less than zero. This helps in determining which portion of the graph is relevant for our solution.

The coordinate plane is a two-dimensional plane that is defined by two perpendicular lines: the horizontal \( x \)-axis and the vertical \( y \)-axis. The point where these axes intersect is known as the origin, labeled as (0,0).

Each point on the plane can be described by an ordered pair \((x, y)\), where \(x\) is the distance from the \(y\)-axis, and \(y\) is the distance from the \(x\)-axis. Understanding the coordinate plane is crucial when interpreting inequalities, as it allows you to visualize which sections of the plane satisfy the inequality.

For the inequality \( y < 0 \), we focus on areas below the \( x \)-axis because only in this part of the coordinate plane can \( y \) be negative.

The solution region is the part of the graph that satisfies the given inequality. To find this region, you need to follow a few important steps:

• First, identify the boundary line. In our example, this is the line \( y = 0 \). Since the inequality involves just 'less than', the line will be dashed, showing that points on this line are not included in the solution region.
• Next, determine where the inequality holds true. For \( y < 0 \), this is anywhere \( y \) is negative.
• Finally, shade the correct region. In this case, the area below the dashed line \( y = 0 \) is shaded, representing all \( y < 0 \).

The solution region visually demonstrates all possible combinations that satisfy the inequality, providing a clear picture that complements the numeric expression.