since line A is perpendicular to the line $y= - \frac{1}{5}x$,

so slope for line A = 5 (Since the slope of a line perpendicular to a given line is the negative inverse of the slope of the other line)

Now two points of the line a are given as (3 , -10)

Putting them in the line equation

y = mx + c

or -10 = 5 * 3 + c

or c = -25

therefore the equation of line A : y = 5x - 25