`(1, 4), y = 4x + 2` Find the distance between the point and the line.

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.