Let A(1,5) andu(3,2)

M(x,y) is on the line passing through A with directionumeans that exists k real such asAM= ku

Coordinates give the system

x - 1 = 3k

y - 5 = 2k

Parametric equation of the line is the system

x = 3k + 1

y = 2k + 5

To get the cartesian equation you have to eliminate k

2x = 6k + 2

3y = 6k + 15

Difference gives 2x - 3y = -13

A cartesian equation is therefore 2x - 3y + 13 = 0