Let us solve for the slope(m)
The slope formula is,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]Given:
[tex]\begin{gathered} (x_1,y_1)=(-3,1) \\ (x_2,y_2)=(4,-2) \end{gathered}[/tex]Therefore,
[tex]m=\frac{-2-1}{4--3}=\frac{-3}{4+3}=-\frac{3}{7}[/tex]Perpendicular law
[tex]\begin{gathered} m_1m_2=-1 \\ \therefore m_2=-\frac{1}{m_1} \end{gathered}[/tex]Hence,
[tex]\begin{gathered} m_2=-\frac{1}{-\frac{3}{7}}=-(1\div-\frac{3}{7})=-(1\times-\frac{7}{3})=\frac{7}{3} \\ \therefore m_2=\frac{7}{3} \end{gathered}[/tex]Therefore, the formula for the equation of the line given a point is,
[tex]y-y_1=m(x-x_1)[/tex]Point
[tex](3,2)[/tex]Therefore,
[tex]\begin{gathered} y-2=\frac{7}{3}(x-3) \\ y=\frac{7}{3}(x-3)+2 \\ y=\frac{7}{3}x-7+2 \\ y=\frac{7}{3}x-5 \end{gathered}[/tex]Hence, the answer is
[tex]y=\frac{7}{3}x-5[/tex]