Problem 536 Graph the linear inequality \(y ... [FREE SOLUTION]

Chapter 4: Problem 536

Graph the linear inequality \(y \geq-2\)

Short Answer

Expert verified

Graph the line \( y = -2 \) and shade above it.

Step by step solution

Identify the Boundary Line

The inequality given is \( y \geq -2 \). Start by identifying the boundary line, which is \( y = -2 \). This is a horizontal line crossing the y-axis at -2.

Draw the Boundary Line

Graph the boundary line \( y = -2 \). Since the inequality is \( \geq \), draw a solid line to show that points on the line are included in the solution.

Determine the Solution Region

The inequality \( y \geq -2 \) means that the region above the line \( y = -2 \) is included in the solution. Shade the area above the boundary line to represent this region.

Verify a Point

To confirm, choose a point in the shaded region, such as \( (0, 0) \). Substitute \( (0, 0) \) into the inequality: \( 0 \geq -2 \). This is true, verifying the correct region is shaded.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

boundary line

In graphing linear inequalities, identifying the boundary line is a crucial step. The boundary line for an inequality separates the solutions of the inequality from the non-solutions. In the given inequality, \( y \geq -2 \), the boundary line comes from the equation \( y = -2 \). This line is horizontal, crossing the y-axis at -2. To draw this line on a graph, you simply draw a straight line parallel to the x-axis at the point where y equals -2. Remember, because the inequality is \( \geq \), the line should be solid, indicating that points on the line are part of the solution set.

solution region

Once the boundary line is drawn, determining the solution region is the next step. The inequality \( y \geq -2 \) tells us that the solution region includes all points where y is greater than or equal to -2. In simpler terms, this means all the points above the boundary line. So, shade the area above the boundary line. This shading represents all the points that satisfy the inequality. It is the visual representation of the solution set.

verifying points

To ensure that the correct region has been shaded, verifying points is essential. Pick any point in the shaded region and test it in the original inequality. For example, if we choose the point \( (0, 0) \), substitute x and y into the inequality: \( 0 \geq -2 \). Since this inequality holds true, it confirms that the point \( (0, 0) \), and thus the shaded region, correctly represents the solution set. This step helps to avoid errors and reassures that the graphing is accurate. Always verify with at least one point in the shaded region.

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91影视

Graph the linear inequality \(y \geq-2\)

Short Answer

Step by step solution

Identify the Boundary Line

Draw the Boundary Line

Determine the Solution Region

Verify a Point

Key Concepts

boundary line

solution region

verifying points

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