The slope of a line passing through (x1, y1) and (x2, y2) is (y2 - y1)/(x2 - x1)
Here the line passes through (a-4, b+4) and (a, b).
The slope of the line is (b + 4 - b)/(a - 4 - a)
The slope of the line is -1.
The slope of the line that passes through 2 given points has the formula:
We'll put x1 = a-4, y1 = b+4 and x2 = a, y2 = b.
We'll substitute them in the formula of the slope:
m = [b-(b+4)]/[a - (a-4)]
We'll remove the brackets and we'll get:
m = (b-b-4)/(a-a+4)
We'll eliminate like terms and we'll have:
m = -4/4
m = -1
The slope of the line that passes through the given points is m = -1.