Answer :
The point of intersection is the point at which two equations have the same values. So, the x coordinate can be found by equating the two equations.
[tex]\begin{gathered} \text{Given f(x)=2x+6 and g(x)=-3x+1} \\ At\text{ the point of intersection, } \\ f(x)=g(x) \\ \text{2x+6}=-3x+1 \\ 2x+3x=1-6 \\ 5x=-5 \\ x=\frac{-5}{5}=-1 \end{gathered}[/tex]The x coordinate at the point of intersection is -1.