Determine the linear function determined by the points (1,2) and (3,5).

The linear function determined by the points (1,2) and
(3,5) is the line passing through these two points .

We
know that the line passing through (x1, y1) and (x2, y2)
is

y-y1 = {(y2-1)/(x2-x1)}
{x-x1).

So the line passing throggh (1,2) and (3,5)
is

y- 2 = {
(5-2)/(3-1)}(x-1).

y-2 =
(3/2)(x-1).

2(y-2) =
3(x-1).

2y-4 = 3x-3.

3x-2y
-3+4 = 0.

3x-2y +1 =
0.

Therefore, the linear function determind by the points
(1,2) and (3, 5) is 3x-2y +1 = 0.