What Is The X-intercept Of The Function $2x - 3y = 12$?A. (0, 6) B. (6, 0) C. (-4, 0) D. (0, -4)

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Understanding the Concept of x-intercept

The x-intercept of a function is the point at which the graph of the function crosses the x-axis. In other words, it is the point where the value of y is equal to zero. To find the x-intercept of a linear function, we need to set y equal to zero and solve for x.

Finding the x-intercept of the given function

The given function is 2x−3y=122x - 3y = 12. To find the x-intercept, we need to set y equal to zero and solve for x. We can do this by substituting y = 0 into the equation and solving for x.

Step 1: Substitute y = 0 into the equation

2x−3(0)=122x - 3(0) = 12

Step 2: Simplify the equation

2x=122x = 12

Step 3: Solve for x

x=122x = \frac{12}{2}

x=6x = 6

Conclusion

The x-intercept of the function 2x−3y=122x - 3y = 12 is (6, 0). This means that the graph of the function crosses the x-axis at the point (6, 0).

Comparison with the given options

The x-intercept of the function 2x−3y=122x - 3y = 12 is (6, 0). Let's compare this with the given options:

  • A. (0, 6) - This is not the x-intercept of the function.
  • B. (6, 0) - This is the x-intercept of the function.
  • C. (-4, 0) - This is not the x-intercept of the function.
  • D. (0, -4) - This is not the x-intercept of the function.

Final Answer

The final answer is B. (6, 0).

Importance of x-intercept in Mathematics

The x-intercept of a function is an important concept in mathematics. It is used to determine the point at which the graph of the function crosses the x-axis. This is useful in a variety of applications, such as graphing functions, solving systems of equations, and finding the maximum or minimum value of a function.

Real-world Applications of x-intercept

The x-intercept of a function has many real-world applications. For example, in economics, the x-intercept of a demand curve represents the point at which the quantity demanded of a good is zero. In physics, the x-intercept of a velocity-time graph represents the point at which the velocity of an object is zero.

Conclusion

In conclusion, the x-intercept of the function 2x−3y=122x - 3y = 12 is (6, 0). This is an important concept in mathematics that has many real-world applications. Understanding the x-intercept of a function is crucial in a variety of fields, including economics, physics, and engineering.

Frequently Asked Questions

  • What is the x-intercept of a function?
  • How do you find the x-intercept of a linear function?
  • What is the importance of x-intercept in mathematics?
  • What are some real-world applications of x-intercept?

Answers to Frequently Asked Questions

  • The x-intercept of a function is the point at which the graph of the function crosses the x-axis.
  • To find the x-intercept of a linear function, you need to set y equal to zero and solve for x.
  • The x-intercept of a function is an important concept in mathematics that has many real-world applications.
  • Some real-world applications of x-intercept include graphing functions, solving systems of equations, and finding the maximum or minimum value of a function.

Introduction

The x-intercept of a function is a fundamental concept in mathematics that has many real-world applications. In this article, we will answer some frequently asked questions about the x-intercept of a function, including what it is, how to find it, and its importance in mathematics.

Q1: What is the x-intercept of a function?

A1: The x-intercept of a function is the point at which the graph of the function crosses the x-axis. In other words, it is the point where the value of y is equal to zero.

Q2: How do you find the x-intercept of a linear function?

A2: To find the x-intercept of a linear function, you need to set y equal to zero and solve for x. This can be done by substituting y = 0 into the equation of the function and solving for x.

Q3: What is the importance of x-intercept in mathematics?

A3: The x-intercept of a function is an important concept in mathematics that has many real-world applications. It is used to determine the point at which the graph of the function crosses the x-axis, which is useful in a variety of applications, such as graphing functions, solving systems of equations, and finding the maximum or minimum value of a function.

Q4: What are some real-world applications of x-intercept?

A4: Some real-world applications of x-intercept include:

  • Graphing functions: The x-intercept of a function is used to determine the point at which the graph of the function crosses the x-axis.
  • Solving systems of equations: The x-intercept of a function is used to solve systems of equations by finding the point at which the two functions intersect.
  • Finding the maximum or minimum value of a function: The x-intercept of a function is used to find the maximum or minimum value of a function by determining the point at which the function changes from increasing to decreasing or vice versa.

Q5: How do you find the x-intercept of a quadratic function?

A5: To find the x-intercept of a quadratic function, you need to set y equal to zero and solve for x. This can be done by substituting y = 0 into the equation of the function and solving for x. The x-intercept of a quadratic function can be found using the quadratic formula: x = (-b ± √(b^2 - 4ac)) / 2a.

Q6: What is the difference between the x-intercept and the y-intercept of a function?

A6: The x-intercept of a function is the point at which the graph of the function crosses the x-axis, while the y-intercept of a function is the point at which the graph of the function crosses the y-axis. In other words, the x-intercept is the point where the value of y is equal to zero, while the y-intercept is the point where the value of x is equal to zero.

Q7: How do you find the x-intercept of a function with multiple x-intercepts?

A7: To find the x-intercept of a function with multiple x-intercepts, you need to set y equal to zero and solve for x. This can be done by substituting y = 0 into the equation of the function and solving for x. The x-intercepts of a function with multiple x-intercepts can be found by solving the equation multiple times.

Q8: What is the significance of the x-intercept in physics?

A8: The x-intercept of a function is significant in physics because it represents the point at which the velocity of an object is zero. This is useful in determining the maximum or minimum value of a function, such as the maximum or minimum velocity of an object.

Q9: How do you find the x-intercept of a function with a negative coefficient?

A9: To find the x-intercept of a function with a negative coefficient, you need to set y equal to zero and solve for x. This can be done by substituting y = 0 into the equation of the function and solving for x. The x-intercept of a function with a negative coefficient can be found by solving the equation multiple times.

Q10: What is the importance of x-intercept in economics?

A10: The x-intercept of a function is important in economics because it represents the point at which the quantity demanded of a good is zero. This is useful in determining the maximum or minimum value of a function, such as the maximum or minimum quantity demanded of a good.

Conclusion

In conclusion, the x-intercept of a function is a fundamental concept in mathematics that has many real-world applications. Understanding the x-intercept of a function is crucial in a variety of fields, including economics, physics, and engineering. By answering some frequently asked questions about the x-intercept of a function, we hope to have provided a better understanding of this important concept.