On A Piece Of Paper, Graph $y \geq 2x - 3$. Then Determine Which Answer Choice Matches The Graph You Drew.A. Graph D B. Graph A C. Graph C D. Graph B

Feb 26, 2025 by ADMIN 155 views

$On a Piece of Paper, Graph $y \geq 2x - 3$ and Determine the Matching Answer Choice$

Introduction

Graphing a linear inequality on a piece of paper can be a straightforward process, but it requires a clear understanding of the inequality's components and how they relate to the graph. In this article, we will explore the process of graphing the linear inequality $y \geq 2x - 3$ and determine which answer choice matches the graph.

Understanding the Inequality

The given inequality is $y \geq 2x - 3$ . This is a linear inequality in the slope-intercept form, where the slope is 2 and the y-intercept is -3. The inequality sign indicates that the graph will be a line or a collection of lines that satisfy the inequality.

Graphing the Inequality

To graph the inequality, we need to find the boundary line, which is the line that separates the region where the inequality is true from the region where it is false. The boundary line is given by the equation $y = 2x - 3$ . We can graph this line by plotting two points on the line and drawing a line through them.

Finding the y-Intercept

The y-intercept of the boundary line is -3, which means that the line crosses the y-axis at the point (0, -3). We can plot this point on the graph.

Finding the x-Intercept

To find the x-intercept, we need to set y equal to 0 and solve for x. This gives us the equation $0 = 2x - 3$ , which simplifies to $2x = 3$ and then $x = \frac{3}{2}$ . We can plot this point on the graph.

Plotting the Line

With the two points plotted, we can draw a line through them to represent the boundary line.

Graphing the Inequality

Now that we have the boundary line, we can graph the inequality by shading the region on one side of the line. Since the inequality is $y \geq 2x - 3$ , we will shade the region above the line.

Determining the Matching Answer Choice

We have graphed the inequality $y \geq 2x - 3$ and shaded the region above the boundary line. Now, we need to determine which answer choice matches this graph.

Answer Choices

We have four answer choices: Graph A, Graph B, Graph C, and Graph D. We need to examine each graph and determine which one matches the graph we drew.

Graph A

Graph A is a line with a positive slope and a y-intercept of -3. However, the line does not have the same slope as the boundary line, and the region above the line is not shaded.

Graph B

Graph B is a line with a positive slope and a y-intercept of -3. However, the line has a different slope than the boundary line, and the region above the line is not shaded.

Graph C

Graph C is a line with a positive slope and a y-intercept of -3. The line has the same slope as the boundary line, and the region above the line is shaded.

Graph D

Graph D is a line with a positive slope and a y-intercept of -3. However, the line does not have the same slope as the boundary line, and the region above the line is not shaded.

Conclusion

Based on our analysis, we can conclude that the graph that matches the inequality $y \geq 2x - 3$ is Graph C. This graph has the same slope as the boundary line and the region above the line is shaded, indicating that the inequality is satisfied.

Final Answer

The final answer is Graph C.

Additional Tips and Tricks

When graphing a linear inequality, it's essential to find the boundary line and determine which region is shaded.
The slope of the boundary line is the same as the slope of the line in the inequality.
The y-intercept of the boundary line is the same as the y-intercept of the line in the inequality.
When shading the region, make sure to shade the region above the line for inequalities of the form $y \geq mx + b$ .

Frequently Asked Questions

Q: What is the boundary line for the inequality $y \geq 2x - 3$ ? A: The boundary line is given by the equation $y = 2x - 3$ .
Q: How do I determine which region is shaded for a linear inequality? A: To determine which region is shaded, find the boundary line and examine the inequality sign. If the inequality sign is $\geq$ , shade the region above the line.
Q: What is the significance of the slope in a linear inequality? A: The slope of the boundary line is the same as the slope of the line in the inequality. This indicates the direction of the line and the region that is shaded.

References

[1] Linear Inequalities. (n.d.). Retrieved from https://www.mathsisfun.com/inequalities/linear-inequalities.html
[2] Graphing Linear Inequalities. (n.d.). Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4/graphing-linear-inequalities/v/graphing-linear-inequalities

Note: The references provided are for general information and are not specific to the article.

Introduction

Graphing linear inequalities can be a challenging task, but with the right guidance, it can be made easier. In this article, we will address some of the most frequently asked questions about graphing linear inequalities.

Q&A

Q: What is the boundary line for a linear inequality?

A: The boundary line for a linear inequality is the line that separates the region where the inequality is true from the region where it is false. It is given by the equation y = mx + b, where m is the slope and b is the y-intercept.

Q: How do I determine which region is shaded for a linear inequality?

A: To determine which region is shaded, find the boundary line and examine the inequality sign. If the inequality sign is ≥, shade the region above the line. If the inequality sign is ≤, shade the region below the line.

Q: What is the significance of the slope in a linear inequality?

A: The slope of the boundary line is the same as the slope of the line in the inequality. This indicates the direction of the line and the region that is shaded.

Q: How do I graph a linear inequality with a negative slope?

A: To graph a linear inequality with a negative slope, follow the same steps as graphing a linear inequality with a positive slope. However, the boundary line will have a negative slope, and the region that is shaded will be below the line.

Q: Can I use a graphing calculator to graph a linear inequality?

A: Yes, you can use a graphing calculator to graph a linear inequality. However, make sure to enter the inequality in the correct format and adjust the window settings as needed.

Q: How do I determine the x-intercept of a linear inequality?

A: To determine the x-intercept of a linear inequality, set y equal to 0 and solve for x. This will give you the x-coordinate of the point where the line crosses the x-axis.

Q: Can I graph a linear inequality with a fractional slope?

A: Yes, you can graph a linear inequality with a fractional slope. However, make sure to simplify the slope fraction and adjust the graph accordingly.

Q: How do I graph a linear inequality with a vertical line?

A: To graph a linear inequality with a vertical line, set x equal to a constant value and solve for y. This will give you the equation of the vertical line, and you can graph it accordingly.

Q: Can I use a graphing software to graph a linear inequality?

A: Yes, you can use a graphing software to graph a linear inequality. However, make sure to enter the inequality in the correct format and adjust the settings as needed.

Additional Tips and Tricks

When graphing a linear inequality, make sure to find the boundary line and determine which region is shaded.
The slope of the boundary line is the same as the slope of the line in the inequality.
The y-intercept of the boundary line is the same as the y-intercept of the line in the inequality.
When shading the region, make sure to shade the region above the line for inequalities of the form y ≥ mx + b.
Use a graphing calculator or software to graph a linear inequality if you are unsure about the graph.

Frequently Asked Questions (FAQs)

Q: What is the boundary line for a linear inequality? A: The boundary line for a linear inequality is the line that separates the region where the inequality is true from the region where it is false.
Q: How do I determine which region is shaded for a linear inequality? A: To determine which region is shaded, find the boundary line and examine the inequality sign.
Q: What is the significance of the slope in a linear inequality? A: The slope of the boundary line is the same as the slope of the line in the inequality.

References

[1] Linear Inequalities. (n.d.). Retrieved from https://www.mathsisfun.com/inequalities/linear-inequalities.html
[2] Graphing Linear Inequalities. (n.d.). Retrieved from https://www.khanacademy.org/math/algebra/x2f1f4/graphing-linear-inequalities/v/graphing-linear-inequalities

Note: The references provided are for general information and are not specific to the article.