The Function F F F Is Given As F ( X ) = 2 3 X F(x) = \frac{2}{3} X F ( X ) = 3 2 X . When X = 6 X = 6 X = 6 , What Is The Value Of F ( X F(x F ( X ]?A. 2 2 2 B. 4 4 4 C. 6 6 6 D. 9 9 9
Introduction
In mathematics, a linear equation is a fundamental concept that represents a relationship between two variables, typically denoted as x and y. The function f(x) = (2/3)x is a linear equation where the slope is 2/3 and the y-intercept is 0. In this article, we will explore the value of f(x) when x = 6, and understand the concept of linear equations in a more detailed manner.
Understanding the Function f(x) = (2/3)x
The function f(x) = (2/3)x is a linear equation where the slope is 2/3 and the y-intercept is 0. The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x). In this case, the slope is 2/3, which means that for every unit increase in x, the value of f(x) increases by 2/3.
Evaluating f(x) at x = 6
To evaluate f(x) at x = 6, we need to substitute x = 6 into the function f(x) = (2/3)x. This can be done by multiplying 6 by 2/3.
Calculating f(6)
f(6) = (2/3) * 6 f(6) = 4
Conclusion
In conclusion, when x = 6, the value of f(x) is 4. This is because the function f(x) = (2/3)x is a linear equation with a slope of 2/3, and when x = 6, the value of f(x) is calculated by multiplying 6 by 2/3.
Understanding the Concept of Linear Equations
Linear equations are a fundamental concept in mathematics that represent a relationship between two variables. The function f(x) = (2/3)x is a linear equation where the slope is 2/3 and the y-intercept is 0. The slope of a linear equation represents the rate of change of the dependent variable (y) with respect to the independent variable (x).
Types of Linear Equations
There are two types of linear equations: standard form and slope-intercept form. The standard form of a linear equation is ax + by = c, where a, b, and c are constants. The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.
Graphing Linear Equations
Linear equations can be graphed on a coordinate plane using a variety of methods, including plotting points, using a slope-intercept form, and using a standard form. The graph of a linear equation is a straight line that passes through the origin if the y-intercept is 0.
Applications of Linear Equations
Linear equations have a wide range of applications in mathematics, science, and engineering. Some examples include:
- Modeling population growth
- Describing the motion of objects
- Calculating the area and perimeter of shapes
- Determining the cost of goods and services
Real-World Examples of Linear Equations
Linear equations are used in a variety of real-world applications, including:
- Calculating the cost of goods and services
- Determining the area and perimeter of shapes
- Modeling population growth
- Describing the motion of objects
Conclusion
In conclusion, the function f(x) = (2/3)x is a linear equation with a slope of 2/3 and a y-intercept of 0. When x = 6, the value of f(x) is 4. Linear equations are a fundamental concept in mathematics that represent a relationship between two variables. They have a wide range of applications in mathematics, science, and engineering, and are used to model real-world phenomena.
Final Answer
The final answer is B. 4.
Introduction
In our previous article, we explored the function f(x) = (2/3)x and evaluated its value at x = 6. We found that f(6) = 4. In this article, we will answer some frequently asked questions about linear equations and the function f(x) = (2/3)x.
Q&A
Q: What is a linear equation?
A: A linear equation is a mathematical equation that represents a relationship between two variables, typically denoted as x and y. It is a fundamental concept in mathematics that can be used to model real-world phenomena.
Q: What is the slope of a linear equation?
A: The slope of a linear equation is a measure of how much the dependent variable (y) changes when the independent variable (x) changes by one unit. In the case of the function f(x) = (2/3)x, the slope is 2/3.
Q: What is the y-intercept of a linear equation?
A: The y-intercept of a linear equation is the point where the line intersects the y-axis. In the case of the function f(x) = (2/3)x, the y-intercept is 0.
Q: How do I graph a linear equation?
A: There are several ways to graph a linear equation, including plotting points, using a slope-intercept form, and using a standard form. The graph of a linear equation is a straight line that passes through the origin if the y-intercept is 0.
Q: What are some real-world applications of linear equations?
A: Linear equations have a wide range of applications in mathematics, science, and engineering, including:
- Modeling population growth
- Describing the motion of objects
- Calculating the area and perimeter of shapes
- Determining the cost of goods and services
Q: How do I evaluate the value of a linear equation at a specific point?
A: To evaluate the value of a linear equation at a specific point, you need to substitute the value of x into the equation and solve for y.
Q: What is the difference between a linear equation and a quadratic equation?
A: A linear equation is a mathematical equation that represents a relationship between two variables, typically denoted as x and y. A quadratic equation is a mathematical equation that represents a relationship between two variables, typically denoted as x and y, and has a squared term.
Q: Can you give an example of a linear equation in real-world application?
A: Yes, here is an example of a linear equation in real-world application:
- A company sells x units of a product at a price of $y per unit. The total revenue is given by the equation y = 2x + 100, where x is the number of units sold and y is the total revenue.
Q: How do I determine the slope and y-intercept of a linear equation?
A: To determine the slope and y-intercept of a linear equation, you need to rewrite the equation in slope-intercept form, which is y = mx + b, where m is the slope and b is the y-intercept.
Conclusion
In conclusion, the function f(x) = (2/3)x is a linear equation with a slope of 2/3 and a y-intercept of 0. We have answered some frequently asked questions about linear equations and the function f(x) = (2/3)x. We hope that this article has provided you with a better understanding of linear equations and their applications.
Final Answer
The final answer is B. 4.