# get points out of two lines where y distance is given value

there are two lines form 3 point like so

Point 1 (1,2)

Point 2 (5,6)

Point 3 (7,1)

Lines are from

1 to 2

and from

1 to 3

what i need are the points on each line where the y (vertical) distance is at a given value (as an example 2)

from constracting this figure i've got on Line 1 to 2 an approximate Point (2.8,3.8) and on Line 1 to 3 an approximate Point (2.8,0.8)

is there a mathematically to solve this, I will need this for a given x value as well?

Let the co-ordinates of two points be $A(x_1, y_1)$ and $B(x_2, y_2)$. The equation of the line AB is given by the “two point form”, which is:-
$\dfrac {y – y_1}{x – x_1} = \dfrac {y_2 – y_1}{x_2 – x_1}$; where (x, y) represents any particular point on that line.