Point j(-2,1) and point k(4,5) form line segment jk. for the point p that partitions jk in the ratio 3: 7, what is the y coordinate for p?

2.2

If we let y represent the value of interest then the requirement for P tells us ...

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

We can multiply by 7(5-y) to get

... 7(y -1) = 3(5 -y)

... 7y -7 = 15 -3y . . . . . eliminate parentheses

... 10y = 22 . . . . . . . . . add 3y+7, then divide by the coefficient of y to get ...

... y = 2.2 . . . . . the y-coordinate for P