Precalculus, Chapter 10, 10.1, Section 10.1, Problem 64

The formula to determine the distance from a point (xo,yo) 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=-2x-3
2x+y+3=0
Then, plug-in the coefficients of x and y, as well as the constant to the formula.
d=|2x_o +1y_o +3|/sqrt(2^2+1^2)
d=|2x_o + y_o +3|/sqrt5
And, plug-in the given point (4,-4).
d=|2(4)+(-4)+3|/sqrt5
d=7/sqrt5
d=7/sqrt5*sqrt5/sqrt5
d=(7sqrt5)/5
Therefore, the point (4,-4) is (7sqrt5)/5 units away from the line y=-2x-3.