When the given line is in standard form or general form (as here), the desired line can be found by replacing the constant by zero, and then translating the line to the given point.
The starting point for your solution can be
7(x-7) - 5(y-9) = 0
In general form, this is
7x - 5y - 4 = 0
In point-slope form, this is
y - 9 = (7/5)(x - 7)
