we must find a line perpendicular to
[tex]y=2x-42[/tex]which passes through (-6,8). As we can see, this given lines has slope m=2.
First, the slope of a perpendicular line is the reciprocal inverse of the given line. In other words,
the perpendicular lines must have slope M equal to
[tex]M=-\frac{1}{m}[/tex]In our case m=2, hence, the perpendicular line has slope
[tex]M=-\frac{1}{2}[/tex]Therefore, the perpendicular line has the form
[tex]y=-\frac{1}{2}x+b[/tex]and now, we must find the y-intercept b. This can be done by substituying the given point (-6,8)
into the last equation:
[tex]8=-\frac{1}{2}(-6)+b[/tex]which gives
[tex]\begin{gathered} 8=\frac{6}{2}+b \\ 8=3+b \\ b=8-3 \\ b=5 \end{gathered}[/tex]Finally, the answer is
[tex]y=-\frac{1}{2}x+5[/tex]