Write the standard form of the equation of the line passing through the point (2,5) and perpendicular to the line 4x - y = 2. the answer key says that the answer is x + 4y = 22, but i'm confused on how to get there

The gradient of the original line is 4. For a perpendicular gradient, you use the negative reciprocal, which is -1/4. Using y - y1 = m(x - x1), you can solve that y - 5 = -(1/4)(x - 2).
Multiply through by -4, you get -4y + 20 = x - 2, which can be rearranged as x + 4y = 22