I find it simplest to convert to standard form, find the perpendicular, convert back.
[tex] y = -4x - 1[/tex]
For standard form we move the x term to the left side:
[tex]4x + y = -1[/tex]
The perpendiculars are given by swapping the x and y coefficients, negating one. The right side is directly determined by the point (-2,7):
[tex]x - 4y = -2 - 4(7) = -30[/tex]
Solve for y for point slope form:
[tex]4y = x + 30[/tex]
[tex]y = \frac 1 4 x + \frac{15}{2}[/tex]
That's the answer.
