Question

Consider the line 5x-8y=8 what is the slope of a line perpendicular to this line what is the slope of a line parallel to this line?

Answer 1

$\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2,\ \text{then}\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\l\ \parallel\ k\iff m_1=m_2\\\\\text{Convert the equation to the slope-intercept form}\ y=mx+b.\\\\5x-8y=8\qquad\text{subtract}\ 5x\ \text{from both sides}\\\\-8y=-5x+8\qquad\text{divide both sides by (-8)}\\\\y=\dfrac{5}{8}x-1\to m_1=\dfrac{5}{8}\\\\perpendicular:\ m_2=-\dfrac{1}{\frac{5}{8}}=-\dfrac{8}{5}\\\\parallel:\ m_2=\dfrac{5}{8}$