Ef is tangent to circle p at g (1,-3). if the slope of ef is 7/9, what is the slope of gp?

The center of the circle is at P. 
The tangent EF is tangent to the circle at point G. So GP will be the radius of the circle. 

The slope of tangent EF = 7/9

The tangent of a circle is always perpendicular to the radius at the point where it touches the circle. So we can say that EF is perpendicular to GP.

The product of slopes of two perpendicular line is always equal to -1.

Slope of EF x Slope of GP = -1
So,

Slope of GP = - 1 / (Slope of EF)

Thus slope of GP = - 9/7