Find m if the point (6,m) is on the line that pass through points (2,4) and (8,8)?

Find m if the point (6,m) is on the line that pass through
points (2,4) and (8,8).

The line passing through the given
points A(2,4) and B(8,8) is given by:

y-yA =
{(yB-yA)/(xB-xA){x-xA).

y-4 =
{(8-4)/(8-2)}(x-2).

y-4 =
(4/6)(x-2).

y-4 =
(2/3)(x-2).

3(y-4) =
2(x-2).

3y -12 = 2x- 4.

3y =
2x-4+12 = 2x+8.

3y= 2x+8 is the line that passes through
A(2,4) and B(8,8).

Since C(6,m) lies on this line 3y=2x+8,
the point the coordinates of C(6,m) should satisfy
3y=2x+8:

=> 3m =
2*6+8

=> 3m =
20

=> m =
20/3.

Therefore the value of m =
20/3.