Given the a line passes through points (1, 1) and ( 7, -5) i.e
[tex]\begin{gathered} (x_1,y_1)\Rightarrow(1,1) \\ (x_2,y_2)\Rightarrow(7,-5) \end{gathered}[/tex]The formula to find the equation of a straight line is
[tex]\frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1}[/tex]Substitute the values into the formula above
[tex]\begin{gathered} \frac{y-y_1}{x-x_1}=\frac{y_2-y_1}{x_2-x_1} \\ \frac{y-1}{x-1}=\frac{-5-1}{7-1} \end{gathered}[/tex]Solve for y
[tex]\begin{gathered} \frac{y-1}{x-1}=\frac{-5-1}{7-1} \\ \frac{y-1}{x-1}=\frac{-6}{6} \\ \frac{y-1}{x-1}=\frac{-1}{1} \\ \text{Crossmultiply} \\ 1(y-1)=-1(x-1) \\ y-1=-x+1 \\ y=-x+1+1 \\ y=-x+2 \end{gathered}[/tex]Hence, the equation of the line is
[tex]y=-x+2[/tex]