First, lets find the equation of the line that passes through the points (-4,3) and (-3,-5):
[tex]\begin{gathered} slope\colon \\ m=\frac{-5-3}{-3-(-4)_{}}=\frac{-8}{1}=-8 \\ equation\colon \\ y-3=-8(x+4) \\ \Rightarrow y=-8(x+4)+3 \end{gathered}[/tex]then, for the line that passes through (-3,-5) and (1,-4), we have:
[tex]\begin{gathered} slope\colon \\ m=\frac{-4-(-5)}{1-(-3)}=\frac{-4+5}{1+3}=\frac{1}{4} \\ equation\colon \\ y+5=\frac{1}{4}(x+3) \\ \Rightarrow y=\frac{1}{4}(x+3)-5 \end{gathered}[/tex]finally, for the line that passes through (1,-4) and (6,1), we get:
[tex]\begin{gathered} slope\colon \\ m=\frac{1-(-4)}{6-1}=\frac{5}{5}=1 \\ equation\colon \\ y+4=1\cdot(x-1) \\ \Rightarrow y=x-1-4=x-5 \\ y=x-5 \end{gathered}[/tex]therefore, the equations are:
y = -8(x+4) +3
y = 1/4(x+3) -5
y = x-5
