Identifying the Graphed Inequality- A Visual Analysis of the Provided Graph

Which of the following inequalities is graphed below?

When it comes to graphing inequalities, it is essential to understand the characteristics of each inequality and how they are represented on a coordinate plane. In this article, we will analyze a given graph and determine which of the provided inequalities is accurately depicted. By doing so, we can enhance our skills in graphing inequalities and identify the correct representation of the given equation.

In the graph provided, we can observe a half-plane that is shaded in a specific color. This half-plane represents the solution set of the inequality. Our task is to match this graph with one of the given inequalities. Let’s examine each option to determine the correct match.

Option A: y > 2x + 3

This inequality represents a line with a slope of -2 and a y-intercept of 3. The line itself is not included in the solution set, as the inequality uses the strict inequality symbol (>), indicating that the line is not part of the solution. The shaded region above the line would be the solution set. However, the graph provided does not match this inequality, as the shaded region is not above the line.

Option B: y ≤ 2x + 3

This inequality is similar to Option A, but with a different inequality symbol (≤). This means that the line itself is included in the solution set. In the graph, the shaded region is above the line, which matches this inequality. Therefore, Option B is a potential match.

Option C: y < 2x + 3 This inequality represents a line with a slope of -2 and a y-intercept of 3, but with a strict inequality symbol (<). This indicates that the line is not part of the solution set, and the shaded region should be below the line. However, the graph provided does not match this inequality, as the shaded region is not below the line. Option D: y ≥ 2x + 3 This inequality is the opposite of Option B, with a different inequality symbol (≥). This means that the line itself is included in the solution set, and the shaded region should be below the line. However, the graph provided does not match this inequality, as the shaded region is not below the line. After analyzing each option, we can conclude that Option B, y ≤ 2x + 3, is the correct inequality that matches the graph provided. This inequality represents a line with a slope of -2 and a y-intercept of 3, and the shaded region above the line corresponds to the solution set. By understanding the characteristics of each inequality and how they are graphed, we can accurately identify the correct representation of a given equation.