What is the y-coordinate of the point that divides the directed line segment from j to k into a ratio of 2: 3?
a.–6
b.–5
c.5
d.7

Let's call the point that divides the line segment as point P.
Point P divides the line segment into ratio 2:3
The ratio 2:3 means we are dividing the line segment into 2+3=5 equal parts. 

The horizontal distance between the two coordinates is 5
The vertical distance between the two coordinates is 10
Dividing both vertical and horizontal distance into five equal parts, we have a horizontal distance of 1 and a vertical distance of 2. 
Every time we move one unit to the left from point J and two units up, we are dividing the line segment into five equal parts as shown in the picture.
The coordinate of point P that divides the line segment into 2 parts and 3 parts is (-5,5)