The point (3,y) lies on the segment with endpoints (3,1); (7,-5). What is y?

We need to determine the equation of the line that passes
through the points: (3,1); (7,-5).

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

We'll identify the
cordinates:

x1 = 3, x2 = 7

y1
= 1, y2 = -5

We'll substitute into the
formula:

(7-3)/(x - 3) = (-5-1)/(y -
1)

4/(x-3) = -6/(y-1)

We'll
divide by 2:

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

We'll cross
multiply:

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

We'll remove the
brackets:

-3x + 9 = 2y -
2

We'll add 2 both sides:

2y =
-3x + 9 + 2

2y = -3x +
11

We'll divide by 2:

y =
-3x/2 + 11/2

If the point (3,y) is located on the line, y =
-3x/2 + 11/2, then it's coordinates verify the equation of the
line:

y = -3*3/2 + 11/2

y =
-9/2 + 11/2

y = 2/2

y =
1

If  x = 3, the
missing coordinate is y = 1.