Write down the equation of a line whose slope is 3/2 and which passes through point P, where P divides the line segment AB joining A(-2, 6) and B(3, -4) in the ratio 2 : 3.

#### Solution

Suppose that P(x, y) divides the line joining the points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) internally in the ratio m : n.

Then the co-ordinates of P are given by the formula,

`x=(mx_2+nx_1)/(m+n)" and "y=(my_2+ny_1)/(m+n)`

`rArrx=(2(3)+3(-2))/(2+3)" and "y=(2(-4)+3(6))/(2+3)`

`rArrx=0" and "y=(-8+18)/5`

`rArrx=0" and "y=10/5`

`rArrx=0" and "y=2`

Thus P(x, y) ≡ P(0, 2)

Now we need to find the equation of the line

whose slope is m = 3/2 and passing though the point P(x_{1}, y_{1}) ≡ P(0, 2)

is y - y_{1} = m(x - x_{1})

`rArry-2=3/2(x-0)`

`rArr2(y-2)=3(x-0)`

`rArr2y-4=3x`

`rArr3x-2y+4=0`