Find the equation of the line through (1,-5) and (7,1)
write the equation in slope intercept form.
1-(-5)/7-1= 6/6 or 1 as the slope, then
y=x+b
y-(-5)=x+1
y+5=x+1
y=x-4
is this correct?

You got the slope correct m = 1

But when you substituted in 

  y - y1 = m(x - x1)
y - (-5) = 1(x - 1)
y - (-5) = x - 1     <------ you have x + 1 on the right.

 That's your error.

   y + 5 = x - 1
       y = x - 6

Edwin