The equation of a line that passes through two points is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]Plugging the values of the points given we have:
[tex]\begin{gathered} y-4=\frac{-5-4}{0-(-3)}(x-(-3)) \\ y-4=\frac{-9}{3}(x+3) \\ y-4=-3(x+3) \\ y-4=-3x-9 \\ y=-3x-9+4 \\ y=-3x-5 \end{gathered}[/tex]Therefore, the equation of the line is:
[tex]y=-3x-5[/tex]