Answer:
y = -x -1
Step-by-step explanation:
You want an equation of the line parallel to y=-x+8 through point (3, -4).
The parallel line will have the same slope as the given line. That slope is the coefficient of x: -1.
The point-slope form of the equation of a line with slope m through point (h, k) is ...
y -k = m(x -h)
You have m=-1, (h, k) = (3, -4), so the desired line has equation ...
y -(-4) = -1(x -3)
y +4 = -x +3 . . . . . . point-slope form
Add -4 to get this to slope-intercept form.
y = -x -1 . . . . . . . . . slope-intercept form