[tex]\text{Let}\ k:y=m_1x+b_1\ \text{and}\ l:y=m_2x+b_2.\\\\l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}\\\\----------------------\\\\\text{The slope-intercept form:}\ y=mx+b.\\\\\text{We have}\ y=\dfrac{2}{3}x+3\to m_1=\dfrac{2}{3}.\ \text{Therefore}\\\\m_2=-\dfrac{1}{\frac{2}{3}}=-\dfrac{3}{2}\\\\\text{We have the equation}\ y=-\dfrac{3}{2}x+b.[/tex]
[tex]\text{Put the coordinates of the given point (6, -8) to the equation:}\\\\-8=-\dfrac{3}{2}(6)+b\\\\-8=-(3)(3)+b\\\\-8=-9+b\qquad\text{add 9 to both sides}\\\\1=b\to b=1\\\\Answer:\ \boxed{y=-\dfrac{3}{2}x+1}[/tex]
