Let:
[tex]\begin{gathered} (x1,y1)=(6,7) \\ (x2,y2)=(-3,4) \\ \text{The slope m is:} \\ m=\frac{y2-y1}{x2-x1}=\frac{4-7}{-3-6}=\frac{-3}{-9}=\frac{1}{3} \end{gathered}[/tex]Using the point-slope equation:
[tex]\begin{gathered} y-y1=m(x-x1) \\ y-7=\frac{1}{3}(x-6) \\ \text{solve for y:} \\ y-7=\frac{1}{3}x-2 \\ y=\frac{1}{3}x-2+7 \\ y=\frac{1}{3}x+5 \end{gathered}[/tex]