How do i write an equation in slope intercept form that passes through point (-7,6) and is perpendicular to line with slope -3/7

When two lines are perpendicular, their slopes are negative reciprocals.

That means that the slope of one line is  -1/(slope of the other line).

You have the slope of one line.  It's  -3/7 .

So the slope of any line perpendicular to that one is  7/3 .

Now you know the slope of the new line, and you know one point on it.

                     Slope  =  7/3
    Through the point  (-7, 6)

I'm pretty sure you know how to do the rest.
The trick was knowing how to find the slope of the new line.