If the new line passes through the point (-6, 2), let's use x = -6 and y = 2 in the equation and then solve it for 'a':
[tex]\begin{gathered} y=\frac{1}{2}x+a\\ \\ 2=\frac{1}{2}(-6)+a\\ \\ 2=-3+a\\ \\ a=2+3\\ \\ a=5 \end{gathered}[/tex]
Therefore the value of 'a' is 5.
