Precalculus, Chapter 10, 10.1, Section 10.1, Problem 68

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.
-2x+y=2
-2x+y-2=0
Then, plug-in the coefficients of x and y, as well as the constant to the formula.
d=|(-2)x_o + 1y_o + (-2)|/sqrt((-2)^2+1^2)
d=|-2x_o + y_o - 2|/sqrt5
And, plug-in the given point (2,1).
d=|-2(2)+1-2|/sqrt5
d=|-5|/sqrt5
d=5/sqrt5
d=5/sqrt5*sqrt5/sqrt5
d=(5sqrt5)/5
d=sqrt5
Therefore, the distance between the point (2,1) and the line is sqrt5 units.