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
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Line A is perpendicular to the line with the equation \(y = - \frac{1}{5} x\) , and the point (3, -10) is on line A. Which of the following is the equation of line A?

A. \(y = - \frac{1}{5} x -\frac{47}{5}\)

B. \(y = \frac{1}{5} x - \frac{53}{5}\)

C. \(y = 5x\)

D. \(y = 5x - 5\)

E. \(y = 5x - 25\)

Slope of perpendicular lines = m1 * m2 = -1

m1 = -(1/5)

Slope of m2 = 5

(y - y1) = m (x - x1)

equate (x1, y1) with (3, -10);

Ans E