Perpendicular to x-6y=7; y-intercept (0,-5). the equation of the line is:

6x +y = -5

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A perpendicular line will have x and y coefficients swapped and one of them negated. A line through (h, k) can be written as
.. a(x -h) +b(y -k) = 0
so your line would be
.. 6(x -0) +1(y -(-5)) = 0
.. 6x +y +5 = 0
.. 6x +y = -5 . . . . . as above