Step-by-step explanation:
the regular slope definition applies :
the slope is the ratio of "y coordinate difference / x coordinate difference". always going from small to large.
so, both segments AB and XY have to have the same slope, as both are on the same line.
when calculating the slope for AB we see that
x changes by +3 (from -6 to -3).
y changes by -2 (from 4 to 2).
the slope is -2/+3 = -2/3
for XY we see
x changes by +9 (from 0 to 9).
y changes by -6 (from 0 to -6).
and the slope is -6/+9 = -2/3
so, yes, as expected, they are the same.
now, if you try and interpret them in the other direction (like going from B to A) we get
x changes by -3 (from -3 to -6).
y changes by +2 (from 2 to 4).
and the slope is +2/-3 = -2/3
as you can see, it is still the same result and slope.
