We need to find the line equation for the line passing through (-1,3) and (5,-5).
First, we need to find the slope using the slope formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1_}[/tex]Replace using P1(-1,3) and P2(5,-5).
Therefore:
[tex]m=\frac{-5-3}{5-(-1)}=\frac{-8}{6}=-\frac{4}{3}[/tex]Then, we need to find the line :
[tex]y-y_1=m(x-x_1)[/tex]Use m= -4/3 and P1(-1,3). Then:
[tex]\begin{gathered} y-3=-\frac{4}{3}(x-(-1)) \\ y-3=-\frac{4}{3}x-\frac{4}{3} \\ y=-\frac{4}{3}x-\frac{4}{3}+3 \\ y=-\frac{4}{3}x+\frac{5}{3} \end{gathered}[/tex]Hence, the line equation is:
[tex]y=-\frac{4}{3}x+\frac{5}{3}[/tex]