The x- intercept of the line joining the points  $\left(3,1\right)$ and $\left(1,3\right)$  is

Equation of the line joining the points $P\left(x_1,y_1\right)$ and $Q\left(x_2,y_2\right)$ is  $\mathrm{y}-{\mathrm{y}}_1=\frac{{\mathrm{y}}_2-{\mathrm{y}}_1}{{\mathrm{x}}_2-{\mathrm{x}}_2}\left(\mathrm{x}-{\mathrm{x}}_1\right)$
Hence the equation of the line joining the points $\left(3,1\right)$  and $\left(1,3\right)$ is  $\mathrm{y}-1=\frac{3-1}{1-3}\left(\mathrm{x}-3\right)$
To get x- intercept, substitute $\mathrm{x}=\mathrm{a},\mathrm{y}=0$ in the above equation  
$\begin{array}{c}0-1=-1\left(\mathrm{a}-3\right)\\ \mathrm{a}=3+1\\ =4\end{array}$ 
Therefore, x-the intercept is $\boxed{4}$