Recall that the slope-intercept form of a line is in the form
[tex]\begin{gathered} y=mx+b \\ \text{where} \\ m\text{ is the slope} \\ b\text{ is the y-intercept} \end{gathered}[/tex]Given the equation x + 8y = 1, convert the equation to slope intercept form
[tex]\begin{gathered} x+8y=1 \\ 8y=-x+1 \\ \frac{8y}{8}=\frac{-x+1}{8} \\ y=-\frac{1}{8}x+\frac{1}{8} \end{gathered}[/tex]Now that it is in the slope intercept form, we have determined that the slope is m = -1/8.
a.) Slope of the line that is parallel
The slope of a line parallel to the given line equation is the same slope to the line, in which case it is m = -1/8.
b.) Slope that is perpendicular to the given line
The slope of a line perpendicular to the given line is the negative reciprocal of the slope.
Solve for the negative reciprocal
[tex]\begin{gathered} m_{\text{parallel}}=-\frac{1}{8} \\ m_{\text{perpendicular}}=-\frac{1}{m_{\text{parallel}}} \\ \\ m_{\text{perpendicular}}=-\frac{1}{-\frac{1}{8}} \\ m_{\text{perpendicular}}=1\cdot\frac{8}{1} \\ m_{\text{perpendicular}}=8 \end{gathered}[/tex]Therefore, the slope perpendicular to the given line is m = 8.
