The perpendicular line to "Y = -4x + 10" that goes the the point (4,-6) is Y = 1/4x + 5.
The slopes are usually a fraction and a whole number. If the first slope is a whole number, it changes to a fraction, and vice versa. Also, if the first slope is negative, the perpendicular slope is positive and vice versa.
The y intercepts in this case are 10 (first slope) and 5 (dividing by 2) since it has to go through (4,-6). See graph below.
I hope this helps!