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].
