To find the value of c, we substitute the point (1,3) on our equation, since the graph of this line passes through this point.

$\displaystyle y=-\frac{1}{2}x+c$

$\displaystyle 3=-\frac{1}{2}\cdot 1+c$

$\displaystyle 3=-\frac{1}{2}+c$

$ \displaystyle c=3+\frac{1}{2}$

$ \displaystyle c=\frac{6}{2}+\frac{1}{2}=\frac{7}{2}$

The final form of our line that is perpendicular with the given line is: $\displaystyle y=-\frac{1}{2}x+\frac{7}{2}$