Given, A line which divides the join of the points (2,3) and ( – 5,8) in the ratio 3:4

To Find : The equation of the line.

Explanation: The coordinates of the point which divides the join of the points (2,3) and ( – 5,8) in the ratio 3:4 is given by (x,y).

Coordinate of x when line divides in ratio m:n

x =

x =

Coordinate of y when line divides in ratio m:n =

y =

y =

The slope of the line with two points is, m =

Now, The slope of joining the points (2,3) and ( – 5,8) =

m =

The equation of the line is

y

y

35y – 180 = 49x + 63

49x – 35y + 229 = 0

Hence, The equation of line is 49x – 35y + 229 = 0