Let's find the [tex]$x$[/tex]-intercept and [tex]$y$[/tex]-intercept of the equation [tex]\(3x + 8y = 24\)[/tex].
### Finding the [tex]$x$[/tex]-Intercept:
The [tex]$x$[/tex]-intercept is the point where the line crosses the [tex]$x$[/tex]-axis. At this point, the value of [tex]$y$[/tex] is [tex]$0$[/tex].
1. Substitute [tex]\(y = 0\)[/tex] into the equation:
[tex]\[
3x + 8(0) = 24
\][/tex]
which simplifies to
[tex]\[
3x = 24.
\][/tex]
2. Solve for [tex]$x$[/tex]:
[tex]\[
x = \frac{24}{3} = 8.
\][/tex]
So, the [tex]$x$[/tex]-intercept is [tex]\(x = 8\)[/tex].
### Finding the [tex]$y$[/tex]-Intercept:
The [tex]$y$[/tex]-intercept is the point where the line crosses the [tex]$y$[/tex]-axis. At this point, the value of [tex]$x$[/tex] is [tex]$0$[/tex].
1. Substitute [tex]\(x = 0\)[/tex] into the equation:
[tex]\[
3(0) + 8y = 24
\][/tex]
which simplifies to
[tex]\[
8y = 24.
\][/tex]
2. Solve for [tex]$y$[/tex]:
[tex]\[
y = \frac{24}{8} = 3.
\][/tex]
So, the [tex]$y$[/tex]-intercept is [tex]\(y = 3\)[/tex].
### Writing the Coordinates of Each Intercept:
- The coordinates of the [tex]$x$[/tex]-intercept are [tex]\((8,0)\)[/tex].
- The coordinates of the [tex]$y$[/tex]-intercept are [tex]\((0,3)\)[/tex].
In summary:
- The [tex]$x$[/tex]-intercept is [tex]\(8\)[/tex]
- The [tex]$y$[/tex]-intercept is [tex]\(3\)[/tex]
