To find the [tex]$x$[/tex]-intercept of the given equation \(4x - 7y = 28\), we follow the steps below:
1. Understanding the [tex]$x$[/tex]-intercept:
The [tex]$x$[/tex]-intercept is the point where the graph of the equation crosses the [tex]$x$[/tex]-axis. At this point, the value of [tex]$y$[/tex] is zero. Thus, we set [tex]$y = 0$[/tex] in the equation to find the corresponding value of [tex]$x$[/tex].
2. Set [tex]$y$[/tex] to zero in the equation:
[tex]\[
4x - 7(0) = 28
\][/tex]
Simplifying this, we get:
[tex]\[
4x = 28
\][/tex]
3. Solve for [tex]$x$[/tex]:
[tex]\[
x = \frac{28}{4}
\][/tex]
[tex]\[
x = 7
\][/tex]
So the coordinate of the [tex]$x$[/tex]-intercept is [tex]\((7, 0)\)[/tex].
