For two perpendicular lines, the product of the slopes equal -1, such that
[tex]m_1\times m_2=-1[/tex]
The main line's equation is given by
[tex]y=-2x+8[/tex]
On comparing with the slope-intercept form of the equation of a line,
[tex]y=mx+c[/tex]
The slope is given as -2.
Hence, the slope of the second line will be
[tex]\begin{gathered} -2\times m_2=-1 \\ m_2=\frac{-1}{-2} \\ m_2=\frac{1}{2} \end{gathered}[/tex]
Next, we check the options to find which has a slope equal to 1/2.
OPTION 1: x - 2y = 6
Rewriting in the slope-intercept form, we have
[tex]\begin{gathered} -2y=-x+6 \\ \text{Dividing through by -2, we have} \\ y=\frac{1}{2}x-3 \end{gathered}[/tex]
Therefore, the slope of the line is 1/2.
Hence, the FIRST OPTION is correct.
