find the coordinates of a point B

Question

Given a point (-2,5), find the coordinates of a point B so that the line segment AB has each slope:
a) 2/3

b) -2/3

Answer 1

The equation of a slope is m = (y2 - y1) / (x2 - x1)------------------> (1)

Substitute m = 2/3 and (x1, y1) = (-2, 5) and (x2, y2) = (x, y) in Equation (1)

2/3   =   (y -  5) / [x- (-2)]

2/3   =   (y -  5) / (x + 2)

2(x + 2)   =   3(y - 5)

2x + 4   =   3y - 15

2x - 3y   =   - 15 - 4

2x - 3y   =   - 19---------------------> (2)

Substitute m = - 2/3 and (x1, y1) = (-2, 5) and (x2, y2) = (x, y) in Equation (1)

-2/3   =   (y -  5) / [x- (-2)]

-2/3   =   (y -  5) / (x + 2)

-2(x + 2)   =   3(y - 5)

-2x - 4   =   3y - 15

2x + 3y   =   15 - 4

2x + 3y   =   11---------------------> (3)

Add equations (2) and (3)

2x - 3y   =   - 19

2x + 3y   =      11

(+)   (+)      (+)

-------------------------------------

4x   =   - 8

x   =  - 2

Substitute x  =  - 2 in equation (3)

2(-2) + 3y  =  11

-4 + 3y   =   11

3y   =   11 + 4

3y   =   15

y   =   5

Th point B is (-2, 5).