Given The Equation $4x - 7y = 28$, Find The Coordinates Of The $x$-intercept.

Introduction

In mathematics, the x-intercept of a linear equation is the point at which the graph of the equation intersects the x-axis. This occurs when the value of y is equal to zero. In this article, we will discuss how to find the x-intercept of a linear equation using the given equation $4x - 7y = 28$.

Understanding the Equation

The given equation is a linear equation in the form of $ax + by = c$, where $a$, $b$, and $c$ are constants. In this case, $a = 4$, $b = -7$, and $c = 28$. To find the x-intercept, we need to set the value of y equal to zero and solve for x.

Setting y Equal to Zero

To find the x-intercept, we set the value of y equal to zero in the given equation. This gives us:

$$4x - 7(0) = 28$$

Simplifying the equation, we get:

$$4x = 28$$

Solving for x

To solve for x, we need to isolate x on one side of the equation. We can do this by dividing both sides of the equation by 4:

$$x = \frac{28}{4}$$

Simplifying the fraction, we get:

$$x = 7$$

Conclusion

Therefore, the coordinates of the x-intercept of the given equation $4x - 7y = 28$ are (7, 0).

Why is the x-Intercept Important?

The x-intercept is an important concept in mathematics because it helps us understand the behavior of linear equations. By finding the x-intercept, we can determine the point at which the graph of the equation intersects the x-axis. This can be useful in a variety of applications, such as graphing linear equations, finding the equation of a line, and solving systems of linear equations.

Real-World Applications

The x-intercept has many real-world applications. For example, in physics, the x-intercept can be used to determine the point at which a projectile intersects the ground. In economics, the x-intercept can be used to determine the point at which a company's revenue intersects the x-axis.

Tips and Tricks

When finding the x-intercept of a linear equation, it's essential to remember to set the value of y equal to zero and solve for x. Additionally, make sure to simplify the equation and isolate x on one side of the equation.

Common Mistakes

One common mistake when finding the x-intercept is to forget to set the value of y equal to zero. This can lead to incorrect solutions. Another common mistake is to not simplify the equation and isolate x on one side of the equation.

Conclusion

In conclusion, finding the x-intercept of a linear equation is a crucial concept in mathematics. By setting the value of y equal to zero and solving for x, we can determine the point at which the graph of the equation intersects the x-axis. This can be useful in a variety of applications, such as graphing linear equations, finding the equation of a line, and solving systems of linear equations.

Final Thoughts

The x-intercept is an essential concept in mathematics that has many real-world applications. By understanding how to find the x-intercept, we can better understand the behavior of linear equations and solve problems in a variety of fields.

References

• [1] "Linear Equations" by Math Open Reference
• [2] "Graphing Linear Equations" by Khan Academy
• [3] "Solving Systems of Linear Equations" by MIT OpenCourseWare

Additional Resources

• [1] "Linear Equations" by Wolfram MathWorld
• [2] "Graphing Linear Equations" by Mathway
• [3] "Solving Systems of Linear Equations" by Purplemath
  Frequently Asked Questions (FAQs) about Finding the x-Intercept ====================================================================

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

A: The x-intercept of a linear equation is the point at which the graph of the equation intersects the x-axis. This occurs when the value of y is equal to zero.

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

A: To find the x-intercept, you need to set the value of y equal to zero in the given equation and solve for x.

Q: What if the equation is in the form of y = mx + b?

A: In this case, you can set the value of y equal to zero and solve for x. This will give you the x-intercept.

Q: Can I use a graphing calculator to find the x-intercept?

A: Yes, you can use a graphing calculator to find the x-intercept. Simply graph the equation and use the calculator to find the point at which the graph intersects the x-axis.

Q: What if the equation has multiple x-intercepts?

A: If the equation has multiple x-intercepts, you will need to find each one separately. This can be done by setting the value of y equal to zero and solving for x for each intercept.

Q: Can I use the x-intercept to find the equation of a line?

A: Yes, you can use the x-intercept to find the equation of a line. If you know the x-intercept and the slope of the line, you can use the point-slope form of a linear equation to find the equation of the line.

Q: What if I have a system of linear equations?

A: If you have a system of linear equations, you can use the x-intercept to find the solution to the system. This can be done by finding the x-intercept of each equation and then solving for the values of x and y that satisfy both equations.

Q: Can I use the x-intercept to solve problems in real-world applications?

A: Yes, you can use the x-intercept to solve problems in real-world applications. For example, in physics, the x-intercept can be used to determine the point at which a projectile intersects the ground. In economics, the x-intercept can be used to determine the point at which a company's revenue intersects the x-axis.

Q: What are some common mistakes to avoid when finding the x-intercept?

A: Some common mistakes to avoid when finding the x-intercept include forgetting to set the value of y equal to zero, not simplifying the equation, and not isolating x on one side of the equation.

Q: How can I practice finding the x-intercept?

A: You can practice finding the x-intercept by working through examples and exercises in a textbook or online resource. You can also use a graphing calculator to graph the equation and find the x-intercept.

Q: What are some additional resources for learning about the x-intercept?

A: Some additional resources for learning about the x-intercept include online tutorials, video lectures, and practice problems. You can also consult with a teacher or tutor for additional help.

Conclusion

In conclusion, finding the x-intercept of a linear equation is a crucial concept in mathematics that has many real-world applications. By understanding how to find the x-intercept, you can better understand the behavior of linear equations and solve problems in a variety of fields.

References

• [1] "Linear Equations" by Math Open Reference
• [2] "Graphing Linear Equations" by Khan Academy
• [3] "Solving Systems of Linear Equations" by MIT OpenCourseWare

Additional Resources

• [1] "Linear Equations" by Wolfram MathWorld
• [2] "Graphing Linear Equations" by Mathway
• [3] "Solving Systems of Linear Equations" by Purplemath