Find The { X$}$- And { Y$}$-intercepts Of The Equation { X - 4y = -8$}$.Provide Your Answer Below:- { X$}$-intercept: { ( \square , 0 )$}$- { Y$}$-intercept: { ( 0 , \square )$}$

Mar 10, 2025 by ADMIN 179 views

**Finding the x- and y-intercepts of a Linear Equation**

Introduction

In mathematics, the x-intercept and y-intercept of a linear equation are the points at which the line crosses the x-axis and y-axis, respectively. These intercepts are crucial in understanding the behavior of a linear equation and are used in various applications, including graphing and solving systems of equations. In this article, we will focus on finding the x- and y-intercepts of the equation x - 4y = -8.

What are x- and y-intercepts?

The x-intercept of a linear equation is the point at which the line crosses the x-axis. At this point, the value of y is always 0. Similarly, the y-intercept is the point at which the line crosses the y-axis. At this point, the value of x is always 0.

Finding the x-intercept

To find the x-intercept of the equation x - 4y = -8, we need to substitute y = 0 into the equation. This is because the x-intercept occurs when y is 0.

Step 1: Substitute y = 0 into the equation

x - 4(0) = -8

Step 2: Simplify the equation

x = -8

Step 3: Write the x-intercept in the form (x, 0)

x-intercept: (-8, 0)

Finding the y-intercept

To find the y-intercept of the equation x - 4y = -8, we need to substitute x = 0 into the equation. This is because the y-intercept occurs when x is 0.

Step 1: Substitute x = 0 into the equation

0 - 4y = -8

Step 2: Simplify the equation

-4y = -8

Step 3: Solve for y

y = 2

Step 4: Write the y-intercept in the form (0, y)

y-intercept: (0, 2)

Conclusion

In this article, we have learned how to find the x- and y-intercepts of a linear equation. We have used the equation x - 4y = -8 as an example and have shown how to substitute y = 0 to find the x-intercept and x = 0 to find the y-intercept. The x-intercept is the point at which the line crosses the x-axis, and the y-intercept is the point at which the line crosses the y-axis. Understanding the x- and y-intercepts of a linear equation is essential in graphing and solving systems of equations.

Key Takeaways

The x-intercept of a linear equation is the point at which the line crosses the x-axis.
The y-intercept of a linear equation is the point at which the line crosses the y-axis.
To find the x-intercept, substitute y = 0 into the equation.
To find the y-intercept, substitute x = 0 into the equation.
The x-intercept is written in the form (x, 0), and the y-intercept is written in the form (0, y).

Practice Problems

Find the x- and y-intercepts of the equation 2x + 3y = 6.
Find the x- and y-intercepts of the equation x - 2y = 4.
Find the x- and y-intercepts of the equation 3x + 2y = 9.

Solutions

x-intercept: (3, 0) y-intercept: (0, 2)
x-intercept: (4, 0) y-intercept: (0, 2)
x-intercept: (3, 0) y-intercept: (0, 3/2)

References

[1] Khan Academy. (n.d.). Linear Equations. Retrieved from https://www.khanacademy.org/math/algebra/x2f8f7d1/x2f8f7d2/x2f8f7d3
[2] Math Open Reference. (n.d.). Linear Equations. Retrieved from https://www.mathopenref.com/linearequations.html
Q&A: Finding the x- and y-intercepts of a Linear Equation ===========================================================

Introduction

In our previous article, we discussed how to find the x- and y-intercepts of a linear equation. In this article, we will answer some frequently asked questions related to finding the x- and y-intercepts of a linear equation.

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

A: The x-intercept of a linear equation is the point at which the line crosses the x-axis. At this point, the value of y is always 0.

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

A: The y-intercept of a linear equation is the point at which the line crosses the y-axis. At this point, the value of x is always 0.

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

A: To find the x-intercept of a linear equation, substitute y = 0 into the equation. This will give you the x-coordinate of the x-intercept.

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

A: To find the y-intercept of a linear equation, substitute x = 0 into the equation. This will give you the y-coordinate of the y-intercept.

Q: What if the equation has a fraction or decimal coefficient?

A: If the equation has a fraction or decimal coefficient, you can still find the x- and y-intercepts by substituting y = 0 and x = 0, respectively. For example, if the equation is 2x + 3y = 6, you can substitute y = 0 to find the x-intercept and x = 0 to find the y-intercept.

Q: Can I use a graphing calculator to find the x- and y-intercepts?

A: Yes, you can use a graphing calculator to find the x- and y-intercepts of a linear equation. Simply graph the equation and use the calculator's built-in functions to find the x- and y-intercepts.

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

A: If the equation has multiple x- and y-intercepts, you can find them by substituting y = 0 and x = 0, respectively, and solving for the other variable. For example, if the equation is x^2 + 4y^2 = 16, you can substitute y = 0 to find the x-intercepts and x = 0 to find the y-intercepts.

Q: Can I use the x- and y-intercepts to graph a linear equation?

A: Yes, you can use the x- and y-intercepts to graph a linear equation. Simply plot the x- and y-intercepts on a coordinate plane and draw a line through them.

Q: What if the equation is not in the standard form (Ax + By = C)?

A: If the equation is not in the standard form (Ax + By = C), you can still find the x- and y-intercepts by rewriting the equation in standard form and then substituting y = 0 and x = 0, respectively.