What Is The Value Of The Function Y = 2 X + 3 Y = 2x + 3 Y = 2 X + 3 When X = − 1 X = -1 X = − 1 ?A. 5 B. 2 C. 1 D. − 5 -5 − 5

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Introduction

In mathematics, functions are used to describe the relationship between two variables. A function is a rule that assigns to each input value, a unique output value. In this article, we will explore the value of the function $y = 2x + 3$ when $x = -1$. This is a simple linear function, and we will use it to demonstrate how to evaluate a function at a given value of the variable.

Understanding the Function

The function $y = 2x + 3$ is a linear function, which means that it can be represented by a straight line. The general form of a linear function is $y = mx + b$, where $m$ is the slope of the line and $b$ is the y-intercept. In this case, the slope is 2 and the y-intercept is 3.

Evaluating the Function

To evaluate the function $y = 2x + 3$ when $x = -1$, we need to substitute $x = -1$ into the function. This means that we will replace $x$ with $-1$ in the equation and solve for $y$.

Step 1: Substitute $x = -1$ into the Function

We will start by substituting $x = -1$ into the function $y = 2x + 3$. This gives us:

$$y = 2(-1) + 3$$

Step 2: Simplify the Equation

Next, we will simplify the equation by evaluating the expression $2(-1)$. This gives us:

$$y = -2 + 3$$

Step 3: Solve for $y$

Finally, we will solve for $y$ by combining the constants on the right-hand side of the equation. This gives us:

$$y = 1$$

Conclusion

In this article, we evaluated the function $y = 2x + 3$ when $x = -1$. We substituted $x = -1$ into the function, simplified the equation, and solved for $y$. The final answer is $y = 1$.

What is the Value of the Function $y = 2x + 3$ when $x = -1$?

The value of the function $y = 2x + 3$ when $x = -1$ is $y = 1$. This is the correct answer.

Why is the Value of the Function $y = 2x + 3$ when $x = -1$ Important?

The value of the function $y = 2x + 3$ when $x = -1$ is important because it demonstrates how to evaluate a linear function at a given value of the variable. This is a fundamental concept in mathematics, and it has many practical applications in fields such as science, engineering, and economics.

How to Evaluate a Linear Function at a Given Value of the Variable

To evaluate a linear function at a given value of the variable, you need to substitute the value of the variable into the function and solve for the output value. This is a simple process that involves basic algebraic manipulations.

What are the Steps to Evaluate a Linear Function at a Given Value of the Variable?

The steps to evaluate a linear function at a given value of the variable are:

1. Substitute the value of the variable into the function.
2. Simplify the equation by evaluating any expressions.
3. Solve for the output value.

What are the Benefits of Evaluating a Linear Function at a Given Value of the Variable?

The benefits of evaluating a linear function at a given value of the variable are:

• It allows you to determine the output value of the function at a specific input value.
• It helps you to understand the relationship between the input and output values of the function.
• It has many practical applications in fields such as science, engineering, and economics.

Conclusion

In this article, we evaluated the function $y = 2x + 3$ when $x = -1$. We substituted $x = -1$ into the function, simplified the equation, and solved for $y$. The final answer is $y = 1$. This demonstrates how to evaluate a linear function at a given value of the variable, which is a fundamental concept in mathematics.

Frequently Asked Questions

Q: What is the value of the function $y = 2x + 3$ when $x = -1$?

A: The value of the function $y = 2x + 3$ when $x = -1$ is $y = 1$.

Q: How do I evaluate a linear function at a given value of the variable?

A: To evaluate a linear function at a given value of the variable, you need to substitute the value of the variable into the function and solve for the output value.

Q: What are the benefits of evaluating a linear function at a given value of the variable?

A: The benefits of evaluating a linear function at a given value of the variable are that it allows you to determine the output value of the function at a specific input value, it helps you to understand the relationship between the input and output values of the function, and it has many practical applications in fields such as science, engineering, and economics.

Q: What is the importance of evaluating a linear function at a given value of the variable?

A: The importance of evaluating a linear function at a given value of the variable is that it demonstrates how to evaluate a linear function at a given value of the variable, which is a fundamental concept in mathematics.

Q: How do I simplify the equation when evaluating a linear function at a given value of the variable?

A: To simplify the equation when evaluating a linear function at a given value of the variable, you need to evaluate any expressions and combine the constants on the right-hand side of the equation.

Q: What are the steps to evaluate a linear function at a given value of the variable?

A: The steps to evaluate a linear function at a given value of the variable are:

1. Substitute the value of the variable into the function.
2. Simplify the equation by evaluating any expressions.
3. Solve for the output value.
   

Introduction

In our previous article, we explored the value of the function $y = 2x + 3$ when $x = -1$. We demonstrated how to evaluate a linear function at a given value of the variable, which is a fundamental concept in mathematics. In this article, we will answer some frequently asked questions about evaluating linear functions.

Q&A: Evaluating Linear Functions

Q: What is the value of the function $y = 2x + 3$ when $x = -2$?

A: To evaluate the function $y = 2x + 3$ when $x = -2$, we need to substitute $x = -2$ into the function and solve for $y$. This gives us:

$$y = 2(-2) + 3$$

Simplifying the equation, we get:

$$y = -4 + 3$$

Solving for $y$, we get:

$$y = -1$$

Therefore, the value of the function $y = 2x + 3$ when $x = -2$ is $y = -1$.

Q: How do I evaluate a linear function at a given value of the variable?

A: To evaluate a linear function at a given value of the variable, you need to substitute the value of the variable into the function and solve for the output value. This involves basic algebraic manipulations, such as simplifying the equation and solving for the output value.

Q: What are the benefits of evaluating a linear function at a given value of the variable?

A: The benefits of evaluating a linear function at a given value of the variable are that it allows you to determine the output value of the function at a specific input value, it helps you to understand the relationship between the input and output values of the function, and it has many practical applications in fields such as science, engineering, and economics.

Q: What is the importance of evaluating a linear function at a given value of the variable?

A: The importance of evaluating a linear function at a given value of the variable is that it demonstrates how to evaluate a linear function at a given value of the variable, which is a fundamental concept in mathematics.

Q: How do I simplify the equation when evaluating a linear function at a given value of the variable?

A: To simplify the equation when evaluating a linear function at a given value of the variable, you need to evaluate any expressions and combine the constants on the right-hand side of the equation.

Q: What are the steps to evaluate a linear function at a given value of the variable?

A: The steps to evaluate a linear function at a given value of the variable are:

1. Substitute the value of the variable into the function.
2. Simplify the equation by evaluating any expressions.
3. Solve for the output value.

Q: Can I use a calculator to evaluate a linear function at a given value of the variable?

A: Yes, you can use a calculator to evaluate a linear function at a given value of the variable. However, it is also important to understand the underlying algebraic manipulations involved in evaluating a linear function.

Q: How do I determine the output value of a linear function at a given value of the variable?

A: To determine the output value of a linear function at a given value of the variable, you need to substitute the value of the variable into the function and solve for the output value.

Q: What are some common mistakes to avoid when evaluating a linear function at a given value of the variable?

A: Some common mistakes to avoid when evaluating a linear function at a given value of the variable include:

• Not substituting the value of the variable into the function
• Not simplifying the equation
• Not solving for the output value
• Not checking the units of the output value

Q: How do I check the units of the output value when evaluating a linear function at a given value of the variable?

A: To check the units of the output value when evaluating a linear function at a given value of the variable, you need to ensure that the units of the input value and the units of the output value are consistent.

Q: What are some real-world applications of evaluating linear functions at given values of the variable?

A: Some real-world applications of evaluating linear functions at given values of the variable include:

• Calculating the cost of goods sold
• Determining the revenue of a business
• Evaluating the performance of a system
• Predicting the behavior of a physical system

Conclusion

In this article, we answered some frequently asked questions about evaluating linear functions. We demonstrated how to evaluate a linear function at a given value of the variable, which is a fundamental concept in mathematics. We also discussed some common mistakes to avoid when evaluating a linear function and some real-world applications of evaluating linear functions.

Frequently Asked Questions

Q: What is the value of the function $y = 2x + 3$ when $x = -3$?

A: To evaluate the function $y = 2x + 3$ when $x = -3$, we need to substitute $x = -3$ into the function and solve for $y$. This gives us:

$$y = 2(-3) + 3$$

Simplifying the equation, we get:

$$y = -6 + 3$$

Solving for $y$, we get:

$$y = -3$$

Therefore, the value of the function $y = 2x + 3$ when $x = -3$ is $y = -3$.

Q: How do I determine the output value of a linear function at a given value of the variable?

A: To determine the output value of a linear function at a given value of the variable, you need to substitute the value of the variable into the function and solve for the output value.

Q: What are some common mistakes to avoid when evaluating a linear function at a given value of the variable?

A: Some common mistakes to avoid when evaluating a linear function at a given value of the variable include:

• Not substituting the value of the variable into the function
• Not simplifying the equation
• Not solving for the output value
• Not checking the units of the output value

Q: How do I check the units of the output value when evaluating a linear function at a given value of the variable?

A: To check the units of the output value when evaluating a linear function at a given value of the variable, you need to ensure that the units of the input value and the units of the output value are consistent.

Q: What are some real-world applications of evaluating linear functions at given values of the variable?

A: Some real-world applications of evaluating linear functions at given values of the variable include:

• Calculating the cost of goods sold
• Determining the revenue of a business
• Evaluating the performance of a system
• Predicting the behavior of a physical system