Using the piecewise definition of the modulus of a function we have:

$\vert \frac{1}{2}x-7\vert=\begin{cases}\hspace{5pt}\frac{1}{2}x-7, &\text{ if }\frac{1}{2}x-7\geq 0\\-\left(\frac{1}{2}x-7\right),&\text{ if }\frac{1}{2}x-7<0\end{cases}$

This simplifies to

$\vert \frac{1}{2}x-7\vert=\begin{cases}\hspace{5pt}\frac{1}{2}x-7, &\text{ if }x\geq 14\\7-\frac{1}{2}x,&\text{ if }x<14\end{cases}$

We can sketch the curve from this or by reflecting the graph of $y=\frac{1}{2}x-7$ across the $x$-axis when it is negative: