Answer:
-3
Explanation:
You want the value of x in (x, -6) so that this point lies on a line with slope 1 through point (4, 1).
Point-slope equation
The point-slope equation for a line with slope m through point (h, k) is ...
y -k = m(x -h)
The line with slope 1 through point (4, 1) can be written as ...
y -1 = 1(x -4)
Application
We want the value of x when y=-6.
y +3 = x . . . . . . . add 4 to solve for x
-6 +3 = x = -3
The value of x is -3.