The slope of this line is
[tex]\dfrac{22-7}{14-3}=\dfrac{15}{11}[/tex]
Using the point-slope formula, the equation of the line is
[tex]y-7=\dfrac{15}{11}(x-3)\implies y=\dfrac{15}{11}x+\dfrac{32}{11}[/tex]
The [tex]x[/tex]-intercept occurs when [tex]y=0[/tex]:
[tex]0=\dfrac{15}{11}x+\dfrac{32}{11}\implies x=-\dfrac{32}{15}[/tex]
so that it has coordinates
[tex]\left(-\dfrac{32}{15},0\right)[/tex]
