To solve this problem, the first step is to find the slope of the line. With the given information, we know that the line is perpendicular to y=-2x+6, find the slope of the line by knowing that the product of the slopes of two perpendicular lines is -1.
[tex]\begin{gathered} m1\cdot m2=-1 \\ -2\cdot m2=-1 \\ m2=-\frac{1}{-2} \\ m2=\frac{1}{2} \end{gathered}[/tex]With this slope and the given point, use the point slope formula to find the equation of the line in slope intercept form.
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-8=\frac{1}{2}(x-(-2)) \\ y-8=\frac{1}{2}(x+2) \\ y-8=\frac{1}{2}x+1 \\ y=\frac{1}{2}x+9 \end{gathered}[/tex]