The coords of the x-intercept are (7,0) and of the y-intercept are (0,-1).
The slope of the line is (-1-0)/(0-7)=1/7, so the slope-intercept equation is:
y-(-1)=(1/7)(x-0), y+1=x/7, y=x/7-1.
We get the same answer if we plug in (7,0):
y=(1/7)(x-7)=x/7-1.