3y + 4x = 8 represents a line on the x-y plane, looking like the image I attached.
To find the x-intercept means to find the place where the line intersects the x-axis. If the line is intersecting the x-axis, then the point where it intersects the x-axis must be a place where y = 0. If y didn't equal 0, then that point wouldn't be on the x-axis.
So, to find the x-intercept, we set y in the given equation to 0, like this:
[tex]3y + 4x = 8
[/tex]
[tex]3(0) + 4x = 8[/tex]
[tex]4x = 8[/tex]
[tex]x = \frac{8}{4}[/tex]
[tex]x=2[/tex]
So, [tex]x=2[/tex]. We assumed that [tex]y=0[/tex] to find the x-intercept at the beginning. Then, our ordered pair in the usual order [tex](x,y)[/tex] is [tex](0,2)[/tex]. You can see this is correct by looking at the attached graph.
