Write the equation for a line that intersects points(1,3) and (2,5)

We need the slope and a point to write an equation.....the slope is

[5-3] / [2 - 1]  = 2/1 = 2

And using the point-slope form, we have

y = 2(x - 1)  + 3 

y = 2x - 2 + 3

y = 2x + 1

Note that we can check this with the other point

y = 2(2) + 1  = 5

So.....when x = 2, y = 5......as expected.......