Given the points (3,1) and (5,-1), we can find the slope with the following formula:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
In this case we have the following:
[tex]\begin{gathered} m=\frac{-1-1}{5-3}=\frac{-2}{2}=-1 \\ m=-1 \end{gathered}[/tex]
now that we have that the slope is m = -1, we can find the equation using the first point and the point-slope formula:
[tex]\begin{gathered} y-y_1=m(x-x_1) \\ \Rightarrow y-1=-1(x-3)=-x+3 \\ \Rightarrow y=-x+3+1=-x+4 \\ y=-x+4 \end{gathered}[/tex]
therefore, the equation of the line is y = -x+4
