To answer this question we will use the following two-point formula for the equation of a line:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1).[/tex]Therefore the equation of the line that passes through the points (1, -3) and (-5,5) is:
[tex]y-(-3)=\frac{5-(-3)}{-5-1}(x-1).[/tex]Simplifying the above result we get:
[tex]\begin{gathered} y+3=\frac{8}{-6}(x-1), \\ y+3=-\frac{4}{3}x+\frac{4}{3}. \end{gathered}[/tex]Subtracting 3 from the above result we get:
[tex]\begin{gathered} y+3-3=-\frac{4}{3}x+\frac{4}{3}-3. \\ y=-\frac{4}{3}x-\frac{5}{3}. \end{gathered}[/tex]Answer:
[tex]y=-\frac{4}{3}x-\frac{5}{3}.[/tex]