What is 9x-7y=-7 in slope intercept form?

Slope intercept form is y = mx + b

So if you start with 9x - 7y = -7, the first thing you need to do is move the 9x to the other side of the equation by subtracting it from both sides.
       9x - 7y =      -7
       -9x          -9x

Now you have -7y = -9x -7

For the equation to be in slope intercept form now you should divide every term by the number in front of your y.  In this case divide every term by -7
    -7y =  -9x  -7
      -7      -7   -7

That leaves you with: y = 9x/7 + 1