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

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

The equation of a line between points (x1, y1) and (x2, y2) is: (y - y1)/(x - x1) = (y2 - y1)/(x2 - x1)

Substituting the values given, the equation of the line is:

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

=> ﻿﻿(y + 5)/(x - 7) = -3/2

As (3,y) lie son this line

(y + 5)/(3 - 7) = -3/2

=> 2y + 10 = -3*-4

=> 2y = 12 - 10

=> 2y = 2

=> y = 1

The required value of y = 1.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

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

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.