Find the point on the line y 6x that is closest to the poin

Find the point on the line y = 6x that is closest to the point P = (2, 6). Point = (, )

Solution

Given the line y =6x, slope is 6.

Perpendicular would have slope = -1/6

then equation of line at (2, 6):

(y - 6) = -(1/6) (x - 2)

6y - 36 = -x + 2

x + 6y = 38

From above we know given equation is y = 6x
Plugging into other equation :

x + 36x = 38

37x = 38

x = 38/37

then y = 6x = 228/37

then the point is (38/37, 228/37).