[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}\ -7x-8y=12.\ \text{Convert to the slope-intercept form:}\\\\-7x-8y=12\qquad\text{add 7x to both sides}\\\\-8y=7x+12\qquad\text{divide both sides by (-8)}\\\\y=-\dfrac{7}{8}x-\dfrac{12}{8}\to m_1=-\dfrac{7}{8}\\\\\text{Therefore}\\\\m_2=-\dfrac{1}{-\frac{7}{8}}=\dfrac{8}{7}[/tex]
[tex]\text{We have the equation of a line:}\\\\y=\dfrac{8}{7}x+b\\\\\text{Put the coordinates of the given point P(-3, 1) to the equation:}\\\\1=\dfrac{8}{7}(-3)+b\\\\1=\dfrac{-24}{7}+b\\\\\dfrac{7}{7}=-\dfrac{24}{7}+b\qquad\text{add}\ \dfrac{24}{7}\ \text{to both sides}\\\\\dfrac{31}{7}=b\\\\Answer:\ \boxed{y=\dfrac{8}{7}x+\dfrac{31}{7}}[/tex]
