jmc

The $x$-axis has equation $y=0$. Thus we need to find out what $x$ is when $y=0$. We notice that the slope of the line is $\frac{9-5}{1-5}=-1$. So to get to $y=1$ we can start at $(9,1)$ and go down one in the $y$ direction. Since the slope of the line is $-1$ we know that going down in $y$ by one results in going up in $x$ by one (i.e. $x$ will be 10). Thus the line intercepts the $x$-axis at $\boxed{(10,0)}$.