Given The Function F ( X ) = − 3 4 X + 2 F(x) = -\frac{3}{4}x + 2 F ( X ) = − 4 3 ​ X + 2 , Find F ( 16 F(16 F ( 16 ].

Introduction

Linear equations 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 a specific type of linear equation, namely the function $f(x) = -\frac{3}{4}x + 2$. We will explore the concept of linear equations, understand the given function, and then proceed to find the value of $f(16)$.

What are Linear Equations?

Linear equations are equations in which the highest power of the variable (in this case, $x$) is 1. They can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants. Linear equations can be solved using various methods, including algebraic manipulation, graphing, and substitution.

Understanding the Given Function

The given function is $f(x) = -\frac{3}{4}x + 2$. This is a linear function, and we can see that the highest power of $x$ is 1. The coefficient of $x$ is $-\frac{3}{4}$, and the constant term is 2.

Solving for $f(16)$

To find the value of $f(16)$, we need to substitute $x = 16$ into the given function. This means we will replace $x$ with 16 in the equation $f(x) = -\frac{3}{4}x + 2$.

def f(x):
    return -3/4 * x + 2
result = f(16)
print(result)

Step-by-Step Solution

Let's break down the solution into smaller steps:

1. Substitute $x = 16$ into the function: Replace $x$ with 16 in the equation $f(x) = -\frac{3}{4}x + 2$.
2. Simplify the expression: Multiply $-\frac{3}{4}$ by 16, and then add 2 to the result.
3. Calculate the final value: Perform the arithmetic operations to find the final value of $f(16)$.

Step 1: Substitute $x = 16$ into the function

$f(16) = -\frac{3}{4}(16) + 2$

Step 2: Simplify the expression

$-\frac{3}{4}(16) = -12$

$f(16) = -12 + 2$

Step 3: Calculate the final value

$f(16) = -10$

Conclusion

In this article, we have solved the linear equation $f(x) = -\frac{3}{4}x + 2$ to find the value of $f(16)$. We have broken down the solution into smaller steps, and used algebraic manipulation to simplify the expression. The final value of $f(16)$ is -10.

Additional Resources

For more information on linear equations and solving them, please refer to the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Frequently Asked Questions

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.

Q: How do I solve a linear equation? A: You can solve a linear equation using algebraic manipulation, graphing, or substitution.

Q: What is the given function? A: The given function is $f(x) = -\frac{3}{4}x + 2$.

$$ $$

Introduction

Linear equations are a fundamental concept in mathematics, and solving them is a crucial skill for students to master. In this article, we will provide answers to some of the most frequently asked questions about linear equations.

Q&A Session

Q: What is a linear equation?

A: A linear equation is an equation in which the highest power of the variable is 1. It can be written in the form $ax + b = c$, where $a$, $b$, and $c$ are constants.

Q: How do I solve a linear equation?

A: You can solve a linear equation using algebraic manipulation, graphing, or substitution. Algebraic manipulation involves rearranging the equation to isolate the variable, graphing involves plotting the equation on a coordinate plane, and substitution involves replacing the variable with a value.

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

A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2. For example, $2x + 3 = 5$ is a linear equation, while $x^2 + 4x + 4 = 0$ is a quadratic equation.

Q: Can I solve a linear equation with fractions?

A: Yes, you can solve a linear equation with fractions. To do so, you need to follow the same steps as solving a linear equation with integers, but you need to be careful with the fractions.

Q: How do I graph a linear equation?

A: To graph a linear equation, you need to plot two points on the coordinate plane that satisfy the equation. You can then draw a line through the two points to represent the equation.

Q: Can I solve a linear equation with variables on both sides?

A: Yes, you can solve a linear equation with variables on both sides. To do so, you need to add or subtract the same value to both sides of the equation to isolate the variable.

Q: What is the slope-intercept form of a linear equation?

A: The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: Can I solve a linear equation with a negative slope?

A: Yes, you can solve a linear equation with a negative slope. To do so, you need to follow the same steps as solving a linear equation with a positive slope, but you need to be careful with the negative sign.

Q: How do I find the x-intercept of a linear equation?

A: To find the x-intercept of a linear equation, you need to set $y = 0$ and solve for $x$.

Q: Can I solve a linear equation with a fraction as the coefficient of the variable?

A: Yes, you can solve a linear equation with a fraction as the coefficient of the variable. To do so, you need to follow the same steps as solving a linear equation with an integer as the coefficient, but you need to be careful with the fraction.

Q: What is the standard form of a linear equation?

A: The standard form of a linear equation is $ax + by = c$, where $a$, $b$, and $c$ are constants.

Q: Can I solve a linear equation with a variable as the coefficient of the variable?

A: Yes, you can solve a linear equation with a variable as the coefficient of the variable. To do so, you need to follow the same steps as solving a linear equation with an integer as the coefficient, but you need to be careful with the variable.

Conclusion

In this article, we have provided answers to some of the most frequently asked questions about linear equations. We hope that this article has been helpful in clarifying any doubts you may have had about linear equations.

Additional Resources

For more information on linear equations and solving them, please refer to the following resources:

• Khan Academy: Linear Equations
• Mathway: Linear Equations
• Wolfram Alpha: Linear Equations

Frequently Asked Questions (FAQs)

Q: What is a linear equation? A: A linear equation is an equation in which the highest power of the variable is 1.

Q: How do I solve a linear equation? A: You can solve a linear equation using algebraic manipulation, graphing, or substitution.

Q: What is the difference between a linear equation and a quadratic equation? A: A linear equation has a highest power of 1, while a quadratic equation has a highest power of 2.

Q: Can I solve a linear equation with fractions? A: Yes, you can solve a linear equation with fractions.

Q: How do I graph a linear equation? A: To graph a linear equation, you need to plot two points on the coordinate plane that satisfy the equation.

Q: Can I solve a linear equation with variables on both sides? A: Yes, you can solve a linear equation with variables on both sides.

Q: What is the slope-intercept form of a linear equation? A: The slope-intercept form of a linear equation is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept.

Q: Can I solve a linear equation with a negative slope? A: Yes, you can solve a linear equation with a negative slope.

Q: How do I find the x-intercept of a linear equation? A: To find the x-intercept of a linear equation, you need to set $y = 0$ and solve for $x$.

Q: Can I solve a linear equation with a fraction as the coefficient of the variable? A: Yes, you can solve a linear equation with a fraction as the coefficient of the variable.

Q: What is the standard form of a linear equation? A: The standard form of a linear equation is $ax + by = c$, where $a$, $b$, and $c$ are constants.

Q: Can I solve a linear equation with a variable as the coefficient of the variable? A: Yes, you can solve a linear equation with a variable as the coefficient of the variable.