Respuesta :
To find the slope of the line given, we write the equation in slope-intercept form:
[tex]y=mx+b[/tex]For the equation,
[tex]3x+8y=1[/tex]subtracting 3x from both sides gives
[tex]8y=1-3x[/tex]Finally, dividing both sides by 8 gives
[tex]y=\frac{1-3x}{8}[/tex]which can be rearranged and written as
[tex]y=-\frac{3}{8}x+\frac{1}{8}[/tex]Hence, the slope of the line parallel to the given line is -3/8.
To find the slope of the perpendicular line, we have to remember that
[tex]m_{\perp}=-\frac{1}{m}[/tex]Since m = -3/8, the above gives
[tex]m_{\perp}=-\frac{1}{(-\frac{3}{8})}[/tex]Simplifying the above gives
[tex]m_{\perp}=\frac{8}{3}[/tex]Hence, the slope of the perpendicular line is 8/3.
