Question

identify an equation in point-slope form for the line perpendicular to y=-4x-1 that passes through (-2,7)

Answer 1

I find it simplest to convert to standard form, find the perpendicular, convert back.

$y = -4x - 1$

For standard form we move the x term to the left side:

$4x + y = -1$

The perpendiculars are given by swapping the x and y coefficients, negating one. The right side is directly determined by the point (-2,7):

$x - 4y = -2 - 4(7) = -30$

Solve for y for point slope form:

$4y = x + 30$

$y = \frac 1 4 x + \frac{15}{2}$

That's the answer.