What Is The { Y $}$-intercept Of The Function { F(x) = -\frac{2}{9} X + \frac{1}{3} $}$?A. { -\frac{2}{9}$}$ B. { -\frac{1}{3}$}$ C. { \frac{1}{3}$}$ D. { \frac{2}{9}$}$

In mathematics, a linear function is a polynomial function of degree one, which means it has the form f(x) = ax + b, where 'a' and 'b' are constants, and 'x' is the variable. The y-intercept of a linear function is the point at which the graph of the function intersects the y-axis. In other words, it is the value of the function when x = 0.

What is the y-intercept of a Linear Function?

The y-intercept of a linear function can be found by substituting x = 0 into the equation of the function. This is because when x = 0, the graph of the function will intersect the y-axis at the point (0, y), where y is the y-intercept.

Finding the y-intercept of the Given Function

The given function is f(x) = -\frac{2}{9} x + \frac{1}{3}. To find the y-intercept, we need to substitute x = 0 into the equation of the function.

f(0) = -\frac{2}{9} (0) + \frac{1}{3} f(0) = 0 + \frac{1}{3} f(0) = \frac{1}{3}

Therefore, the y-intercept of the function f(x) = -\frac{2}{9} x + \frac{1}{3} is \frac{1}{3}.

Conclusion

In conclusion, the y-intercept of a linear function is the point at which the graph of the function intersects the y-axis. It can be found by substituting x = 0 into the equation of the function. In this article, we found the y-intercept of the given function f(x) = -\frac{2}{9} x + \frac{1}{3} to be \frac{1}{3}.

Answer

The correct answer is C. \frac{1}{3}.

Additional Information

• The y-intercept of a linear function is a constant value that represents the point at which the graph of the function intersects the y-axis.
• The y-intercept can be found by substituting x = 0 into the equation of the function.
• The y-intercept is an important concept in mathematics, particularly in algebra and geometry.

Real-World Applications

• The concept of y-intercept has numerous real-world applications, such as:
  • Modeling population growth and decline
  • Analyzing the relationship between variables in economics and finance
  • Understanding the behavior of physical systems, such as the motion of objects under the influence of gravity

Common Mistakes

• Substituting x = 1 instead of x = 0 to find the y-intercept
• Not simplifying the expression after substituting x = 0
• Not checking the units of the answer to ensure it matches the units of the function

Tips and Tricks

• Always substitute x = 0 to find the y-intercept of a linear function.
• Simplify the expression after substituting x = 0 to ensure the answer is in the correct form.
• Check the units of the answer to ensure it matches the units of the function.
  Q&A: Understanding the y-intercept of a Linear Function =====================================================

In the previous article, we discussed the concept of y-intercept in linear functions and found the y-intercept of the function f(x) = -\frac{2}{9} x + \frac{1}{3}. In this article, we will answer some frequently asked questions about the y-intercept of a linear function.

Q: What is the y-intercept of a linear function?

A: The y-intercept of a linear function is the point at which the graph of the function intersects the y-axis. It is the value of the function when x = 0.

Q: How do I find the y-intercept of a linear function?

A: To find the y-intercept of a linear function, you need to substitute x = 0 into the equation of the function. This will give you the value of the function when x = 0, which is the y-intercept.

Q: What is the difference between the y-intercept and the x-intercept?

A: The y-intercept is the point at which the graph of the function intersects the y-axis, while the x-intercept is the point at which the graph of the function intersects the x-axis. The x-intercept is found by substituting y = 0 into the equation of the function.

Q: Can the y-intercept be negative?

A: Yes, the y-intercept can be negative. If the coefficient of x in the equation of the function is negative, the y-intercept will be negative.

Q: Can the y-intercept be a fraction?

A: Yes, the y-intercept can be a fraction. If the equation of the function has a fraction as the coefficient of x, the y-intercept will also be a fraction.

Q: How do I know if the y-intercept is positive or negative?

A: To determine if the y-intercept is positive or negative, you need to look at the equation of the function. If the coefficient of x is positive, the y-intercept will be positive. If the coefficient of x is negative, the y-intercept will be negative.

Q: Can the y-intercept be zero?

A: Yes, the y-intercept can be zero. If the equation of the function is of the form f(x) = 0, the y-intercept will be zero.

Q: What is the significance of the y-intercept in real-world applications?

A: The y-intercept has numerous real-world applications, such as modeling population growth and decline, analyzing the relationship between variables in economics and finance, and understanding the behavior of physical systems, such as the motion of objects under the influence of gravity.

Q: How do I use the y-intercept in real-world applications?

A: To use the y-intercept in real-world applications, you need to substitute the values of the variables into the equation of the function and solve for the y-intercept. This will give you the value of the function at the point where the graph intersects the y-axis.

Q: Can I use the y-intercept to make predictions about the future?

A: Yes, you can use the y-intercept to make predictions about the future. By analyzing the trend of the function and the value of the y-intercept, you can make predictions about the future behavior of the system.

Conclusion

In conclusion, the y-intercept of a linear function is an important concept in mathematics, particularly in algebra and geometry. It has numerous real-world applications and can be used to make predictions about the future behavior of a system. By understanding the concept of y-intercept, you can analyze and solve problems in a variety of fields, including economics, finance, and physics.

Additional Resources

• For more information on the y-intercept of a linear function, please refer to the following resources:
  • Khan Academy: Linear Equations and Functions
  • Mathway: Linear Equations and Functions
  • Wolfram Alpha: Linear Equations and Functions

Common Mistakes

• Substituting x = 1 instead of x = 0 to find the y-intercept
• Not simplifying the expression after substituting x = 0
• Not checking the units of the answer to ensure it matches the units of the function

Tips and Tricks

• Always substitute x = 0 to find the y-intercept of a linear function.
• Simplify the expression after substituting x = 0 to ensure the answer is in the correct form.
• Check the units of the answer to ensure it matches the units of the function.