Question

What is the x-coordinate of the point that divides EF into a 2:3 ratio?

Answer 1

(x-(-4))/(9-x)=2/3
(x+4)/(9-x)=2/3
3(x+4)=2(9-x)
3x+12=18-2x
5x=6
x=6/5 = 1.2

Answer 1.2

Answer 2

Short Answer P(6/5,y) = P(1.2,y)
Remark
This problem is solved by a formula known as the section formula. If you want to divide a line into any ratio other than 1:1, this formula will do it for you.

Givens
Line segment with endpoints (-4,-8) and (9,3)
y2 = 3
y1 = -8
x2 = 9
x1 = - 4
m=2
n = 3
Desired ratio 
    m = 3
    n = 2
m:n = 3:2

Formula
P(x,y) = $P(\frac{m*x2 + n*x1}{m+n}, \frac{m*y2 +n*y1}{m+n} )$

Sub and Solve
P(x,y) = $\frac{2*9 + 3*(-4}{2 + 3}, \frac{2*3 + 3*(-8)}{2 + 3}$
P(x,y) = $\frac{18 - 12 }{5} , \frac{6 - 24}{5}$
P(x,y) $\frac{6}{5} , \frac{-18}{5}$

conclusion
The point you want is 
P(6/5,-18/5) If you measure the length with a ruler, you should see that the ratio the line is cut into is 2 : 3

Note: This question all depends on where you start from and what you call (x1,y1) and (x2,y2). Be prepared to argue the point if this answer is incorrect. Point C on my graph is the answer.