Informally, instead of using formal mathematics -- hoping it will help you understand the formal math....
The slope, "rise over run", is -2/7. That means that whenever x changes by 7 ("the run is 7"), y changes by -2 ("the rise is -2").
From (3,4) to (10,y), x changes by 10-3 = 7 (the run is 7), so the y should change by -2 (the rise is -2). A rise of -2 starting from y=4 puts you at y=2 (4 plus -2 equals 2).