Explore Westonci.ca, the leading Q&A site where experts provide accurate and helpful answers to all your questions. Ask your questions and receive precise answers from experienced professionals across different disciplines. Experience the convenience of finding accurate answers to your questions from knowledgeable experts on our platform.

Find the \( x \)- and \( y \)-intercepts of the equation.

[tex]\[ -6y - 8x = 24 \][/tex]

a. Find the coordinates of the [tex]\( x \)[/tex]-intercept.


Sagot :

To find the \( x \)-intercept of the equation \(-6y - 8x = 24\), follow these steps:

1. Understand the Concept of \( x \)-Intercept:
The \( x \)-intercept is the point where the graph of the equation crosses the \( x \)-axis. At this point, the \( y \)-coordinate is \( 0 \).

2. Set \( y = 0 \):
Substitute \( y = 0 \) into the equation to find the corresponding \( x \)-coordinate.

3. Substitute and Simplify:
[tex]\[ -6(0) - 8x = 24 \][/tex]
[tex]\[ 0 - 8x = 24 \][/tex]
[tex]\[ -8x = 24 \][/tex]

4. Solve for \( x \):
Divide both sides of the equation by \(-8\):
[tex]\[ x = \frac{24}{-8} \][/tex]
[tex]\[ x = -3 \][/tex]

The coordinate of the \( x \)-intercept is \((-3, 0)\).

So, the [tex]\( x \)[/tex]-intercept of the equation [tex]\(-6y - 8x = 24\)[/tex] is [tex]\((-3, 0)\)[/tex].