`(-2, 6), y = -x + 5` 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=-x+5`

`x+y-5=0`

Then, plug-in the coefficients of x and y, as well as the constant to the formula.

`d=|1x_o + 1y_o + (-5)|/sqrt(1^2+1^2)`

`d=|x_o + y_o - 5|/sqrt2`

And, plug-in the given point (-2,6).

`d=|-2 + 6 - 5|/sqrt2`

`d=|-1|/sqrt2`

`d=1/sqrt2`

`d=1/sqrt2*sqrt2/sqrt2`

`d=sqrt2/2`

Therefore, the distance between the point (-2,6) and the line y=-x+5 is `sqrt2/2` units.