What equation of a line passes through ( -6,9) and is perpendicular to (-2,1) and (6,7) All of those^

y = 4/3x + 1.

Step-by-step explanation:

The equation of the lines passing through (2,1) and (6,7) is:

y - 7 = (7-1)/(6- -2)(x - 6)

y - 7 = 6/8(x - 6)

y = 3/4(x - 6) + 7

y = 3/4x + 5/2.

So the line perpendicular to it has slope -1/3/4 = -4/3:

y - 9 = -4/3(x  + 6)

y = -4/3 x  - 8 + 9

y = 4/3x + 1.