To find the slope(m), you use the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1} [/tex]
(-5, -1) = (x₁, y₁)
(5, -7) = (x₂, y₂) [It doesn't matter which point you use for the 1st or 2nd point because it has the same result]
Now substitute/plug the points into the equation:
[tex]m=\frac{y_2-y_1}{x_2-x_1} [/tex]
[tex]m=\frac{-7-(-1)}{5-(-5)} [/tex] [Two negative signs cancel each other out and become positive]
[tex]m=\frac{-7+1}{5+5} [/tex]
[tex]m=\frac{-6}{10} [/tex] Simplify the fraction
[tex]m=-\frac{3}{5} [/tex]