Choose The Correct Answer.Which Coordinate Is A Solution To The Inequality $y \ \textgreater \ -x - 4$?A. $(-4, -4$\] B. $(-4, 4$\] C. $(-4, 0$\] D. $(0, -4$\]

Introduction

Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will focus on solving linear inequalities of the form $y > mx + b$, where $m$ and $b$ are constants. We will use a step-by-step approach to solve the inequality $y > -x - 4$ and determine which coordinate is a solution to this inequality.

Understanding Linear Inequalities

A linear inequality is an inequality that can be written in the form $y > mx + b$, where $m$ and $b$ are constants. The inequality $y > -x - 4$ is a linear inequality, where $m = -1$ and $b = -4$. To solve this inequality, we need to isolate the variable $y$ and determine the values of $x$ and $y$ that satisfy the inequality.

Solving the Inequality

To solve the inequality $y > -x - 4$, we can start by adding $x$ to both sides of the inequality. This gives us:

$$y + x > -4$$

Next, we can subtract $x$ from both sides of the inequality to isolate the variable $y$. This gives us:

$$y > -x - 4$$

However, we can simplify this inequality further by adding $4$ to both sides of the inequality. This gives us:

$$y + 4 > -x$$

Now, we can subtract $4$ from both sides of the inequality to isolate the variable $y$. This gives us:

$$y > -x - 4$$

Graphing the Inequality

To graph the inequality $y > -x - 4$, we can use a graphing calculator or plot the line $y = -x - 4$ on a coordinate plane. The inequality $y > -x - 4$ represents all the points on the coordinate plane that are above the line $y = -x - 4$.

Analyzing the Options

Now that we have graphed the inequality $y > -x - 4$, we can analyze the options to determine which coordinate is a solution to this inequality.

• Option A: $(-4, -4)$

  This point is below the line $y = -x - 4$, so it is not a solution to the inequality $y > -x - 4$.

• Option B: $(-4, 4)$

  This point is above the line $y = -x - 4$, so it is a solution to the inequality $y > -x - 4$.

• Option C: $(-4, 0)$

  This point is below the line $y = -x - 4$, so it is not a solution to the inequality $y > -x - 4$.

• Option D: $(0, -4)$

  This point is below the line $y = -x - 4$, so it is not a solution to the inequality $y > -x - 4$.

Conclusion

In conclusion, the correct answer is Option B: $(-4, 4)$. This point is above the line $y = -x - 4$, so it is a solution to the inequality $y > -x - 4$.

Final Answer

The final answer is $\boxed{B}$.

Additional Resources

For more information on solving linear inequalities, please refer to the following resources:

• Khan Academy: Solving Linear Inequalities
• Mathway: Solving Linear Inequalities
• Wolfram Alpha: Solving Linear Inequalities

FAQs

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form $y > mx + b$, where $m$ and $b$ are constants.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can start by adding or subtracting the same value to both sides of the inequality to isolate the variable $y$.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that can be written in the form $y = mx + b$, where $m$ and $b$ are constants. A linear inequality is an inequality that can be written in the form $y > mx + b$ or $y < mx + b$, where $m$ and $b$ are constants.

Q: How do I graph a linear inequality?

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Introduction

Linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide a comprehensive Q&A guide on solving linear inequalities. We will cover various topics, including the definition of linear inequalities, how to solve them, and how to graph them.

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form $y > mx + b$, where $m$ and $b$ are constants. It is a mathematical statement that compares two expressions and indicates whether one is greater than, less than, or equal to the other.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can start by adding or subtracting the same value to both sides of the inequality to isolate the variable $y$. You can also multiply or divide both sides of the inequality by a non-zero value to simplify the expression.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that can be written in the form $y = mx + b$, where $m$ and $b$ are constants. A linear inequality is an inequality that can be written in the form $y > mx + b$ or $y < mx + b$, where $m$ and $b$ are constants.

Q: How do I graph a linear inequality?

A: To graph a linear inequality, you can use a graphing calculator or plot the line $y = mx + b$ on a coordinate plane. The inequality represents all the points on the coordinate plane that are above or below the line.

Q: What is the solution to a linear inequality?

A: The solution to a linear inequality is the set of all points on the coordinate plane that satisfy the inequality. It is the region of the plane that is above or below the line $y = mx + b$.

Q: How do I determine the solution to a linear inequality?

A: To determine the solution to a linear inequality, you can graph the line $y = mx + b$ on a coordinate plane and shade the region that satisfies the inequality. You can also use algebraic methods to solve the inequality and find the solution.

Q: What are some common types of linear inequalities?

A: Some common types of linear inequalities include:

• Greater than inequalities: $y > mx + b$
• Less than inequalities: $y < mx + b$
• Equal to inequalities: $y = mx + b$

Q: How do I solve a system of linear inequalities?

A: To solve a system of linear inequalities, you can graph the lines $y = mx + b$ on a coordinate plane and find the region that satisfies both inequalities. You can also use algebraic methods to solve the system and find the solution.

Q: What are some real-world applications of linear inequalities?

A: Linear inequalities have many real-world applications, including:

• Finance: Linear inequalities are used to model financial situations, such as investments and loans.
• Science: Linear inequalities are used to model scientific situations, such as population growth and chemical reactions.
• Engineering: Linear inequalities are used to model engineering situations, such as structural analysis and circuit design.

Conclusion

In conclusion, linear inequalities are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. By understanding the definition of linear inequalities, how to solve them, and how to graph them, you can apply linear inequalities to real-world situations and solve complex problems.

Final Answer

The final answer is $\boxed{B}$.

Additional Resources

For more information on solving linear inequalities, please refer to the following resources:

• Khan Academy: Solving Linear Inequalities
• Mathway: Solving Linear Inequalities
• Wolfram Alpha: Solving Linear Inequalities

FAQs

Q: What is a linear inequality?

A: A linear inequality is an inequality that can be written in the form $y > mx + b$, where $m$ and $b$ are constants.

Q: How do I solve a linear inequality?

A: To solve a linear inequality, you can start by adding or subtracting the same value to both sides of the inequality to isolate the variable $y$.

Q: What is the difference between a linear inequality and a linear equation?

A: A linear equation is an equation that can be written in the form $y = mx + b$, where $m$ and $b$ are constants. A linear inequality is an inequality that can be written in the form $y > mx + b$ or $y < mx + b$, where $m$ and $b$ are constants.

Q: How do I graph a linear inequality?

A: To graph a linear inequality, you can use a graphing calculator or plot the line $y = mx + b$ on a coordinate plane. The inequality represents all the points on the coordinate plane that are above or below the line.