The general form of the equation of the line is:
[tex]y=mx+b[/tex]where m is the slope of the line and b the y-intersect. Lines with the same slope are considered parallels between them.
You have a line which is parallel to the line y=-1/7x -1, and tha passes trough the point (2,-1).
The slope of the searched line is m=-1/7. In order to find theequation of the line, you use the following formula for the slope of a line:
[tex]m=\frac{y-y_0}{x-x_0}[/tex]where (x0,y0) is one of the points of the line. In this case you consider this point is (2,-1). You replace these values of the point and the values of the slope into the formula for the slope and you proceed as follow:
[tex]\begin{gathered} m=\frac{y-(-1)}{x-2}=\frac{y+2}{x-2} \\ -\frac{1}{7}=\frac{y+2}{x-2} \\ (-\frac{1}{7})(x-2)=y+2 \\ -\frac{1}{7}x+\frac{2}{7}=y+2 \\ y=-\frac{1}{7}x+\frac{2}{7}-2 \\ y=-\frac{1}{7}x+\frac{2-14}{7} \\ y=-\frac{1}{7}x-\frac{12}{7} \end{gathered}[/tex]The previous equation, is the equation of the searched line.
