Precalculus, Chapter 10, 10.1, Section 10.1, Problem 62

Take note that the formula to determine the distance from a point (x_o, y_o) to a line Ax+By+C=0 is:
d = |Ax_o + By_o +C|/sqrt(A^2+B^2)
To apply, set one side of the given equation equal to zero.
y=4x+2
-4x + y - 2 =0
Then, plug-in the coefficients of x and y, as well as the constant to the formula.
d=|-4x_o + 1y_o + (-2)|/sqrt((-4)^2 + 1^2)
d = |-4x_o + y_o - 2|/sqrt17
And, plug-in the given point (1,4).
d=|-4(1) + 4 - 2|/sqrt17
d=|-2|/sqrt17
d=2/sqrt17
d=2/sqrt17*sqrt17/sqrt17
d=(2sqrt17)/17
Therefore, the distance between the point (1,4) and the line y=4x+2 is (2sqrt17)/17 units.