The slope-point form of the equation of a line with slope m that passes through the point (x_0,y_0), is:
[tex]y=m(x-x_0)+y_0[/tex]To find the equation of the line that contains the point with coordinates (5,-1) and has a slope 1/5, susbtitute x_0=5, y_0=-1 and m=1/5:
[tex]y=\frac{1}{5}(x-5)-1[/tex]The equation can be simplified to be written in slope-intercept form:
[tex]\begin{gathered} \Rightarrow y=\frac{1}{5}x-\frac{1}{5}\times5-1 \\ =\frac{1}{5}x-1-1 \\ =\frac{1}{5}x-2 \end{gathered}[/tex]Therefore, the equation of such a line (in slope-intercept form) is:
[tex]y=\frac{1}{5}x-2[/tex]