The Solution:
Given:
[tex]\begin{gathered} y=-8x+2 \\ \\ Point=(-4,1) \end{gathered}[/tex]
Step 1:
Find the slope of a line that is perpendicular to the given line.
The slope is:
[tex]m_2=\frac{-1}{m_1}[/tex]
Where:
[tex]\begin{gathered} m_1=the\text{ slope of the given line}=-8 \\ m_2=the\text{ slope of a perpendicular line}=? \end{gathered}[/tex][tex]m_2=\frac{-1}{-8}=\frac{1}{8}[/tex]
The formula for the equation of a line is:
[tex]\begin{gathered} y-y_1=m_2(x-x_1) \\ \\ (x_1=-4,y_1=1) \end{gathered}[/tex]
Substitute:
[tex]y-1=\frac{1}{8}(x--4)[/tex][tex]\begin{gathered} y-1=\frac{1}{8}(x+4) \\ \\ y=\frac{1}{8}x+\frac{1}{2}+1 \\ \\ y=\frac{1}{8}x+\frac{3}{2} \end{gathered}[/tex]
Therefore, the correct answer is:
[tex]y=\frac{1}{8}x+\frac{3}{2}[/tex]
