Let the line that passes through the points be y = mx + c where m is the slope of the line and c is the y-intercept.
It passes through (x , y)
=> y = mx + c ...(1)
It passes through (x - 1, (y + 2)
=> y + 2 = mx - m + c ...(2)
(2) - (1)
=> 2 = -m
=> m = -2
The required slope of the line is m = -2
Coordinates : (x-1,y+2) , (x,y)
Gradient(m) = (y₁- y₂) / (x₁- x₂)
m = (y+2-y)/( x-1-x)
m = 2/-1
the slope of the line which passes through coordiantes (x-1,y+2) and (x,y) is m=-2
We'll recall the formula that gives the slope of the line that passes through two points:
Let x1 = x-1, y1 = y+2 and x2 = x, y2 = y.
We'll substitute them in the formula of the slope:
m = [y-(y+2)]/[x - (x-1)]
We'll remove the brackets and we'll get:
m = (y-y-2)/(x-x+1)
We'll eliminate like terms and we'll have:
m = -2/1
m = -2
The required slope of the line that passes through the points (x-1,y+2) and (x,y), is m = -2.