First, let's find the slope m
[tex]m=\frac{-4--(1)}{0-5}\rightarrow m=\frac{-3}{-5}\rightarrow m=\frac{3}{5}[/tex]Now we use the slope-point form to find the equation. Let's use the slope we just calculated an point (5, -1)
[tex]\begin{gathered} y-(-1)=\frac{3}{5}(x-5)\rightarrow y+1=\frac{3}{5}x-3 \\ y=\frac{3}{5}x-4 \end{gathered}[/tex]Therefore, the equation of the line that goes through (5, -1) and (0, -4) is
[tex]y=\frac{3}{5}x-4[/tex]
