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

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We'll determine the equation of the line that passes through the points: (2,4) and (8,8)

(x2 - x1)/(x - x1) = (y2 - y1)/(y - y1)

We'll identify the cordinates:

x1 = 2, x2 = 8

y1 = 4, y2 = 8

We'll substitute into the formula:

(8-2)/(x - 2) = (8-4)/(y - 4)

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

We'll cross multiply:

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

We'll remove the brackets:

4x - 8 = 6y - 24

We'll add 24 both sides:

6y = 4x - 8 + 24

6y = 4x + 16

We'll divide by 6:

y = 2x/3 + 8/3

If the point (6,m) is on the line , then it's coordinates verify the equation of the line:

m = 2*6/3 + 8/3

**m = 20/3**

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.