The points (x-1,y+2) and (x,y) lie on the same line. How to determine the slope of the line?

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justaguide's profile pic

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

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

lochana2500's profile pic

lochana2500 | Student, Undergraduate | (Level 1) Valedictorian

Posted on

Coordinates : (x-1,y+2) , (x,y)

Gradient(m) = (y₁- y₂) / (x₁- x₂)

m = (y+2-y)/( x-1-x)

m = 2/-1

m =(-2)

the slope of the line which passes through coordiantes (x-1,y+2) and (x,y) is m=-2

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll recall the formula that gives the slope of the line that passes through two points:

m=(y2-y1)/(x2-x1)

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.

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