The equation of line between two points is given as:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]plugging the values into the equation we have:
[tex]\begin{gathered} y-(-5)=\frac{1-(-5)}{-5-(-1)}(x-(-1)) \\ y+5=\frac{1+5}{-5+1}(x+1) \\ y+5=\frac{6}{-4}(x+1) \\ y+5=-\frac{6}{4}(x+1) \end{gathered}[/tex]Therefore the equation is:
[tex]y+5=-\frac{3}{2}(x+1)[/tex]