You probably will not like my answe much Sara because I do not do questions like this by formula.
I can never remember formulas that I do not think I really need. It is some weird kind of mental block 
Find the ratio in which the point(-3,k) divides the line segment joining the points (-5,-4) and (-2,3). Also find the value of k.
Look at the x values first
-2--5=3
-3--5=2
so the dividing point is 2/3 of the way starting from the first end point. The ratio is 2:3
so the k value must also be 2/3 of the way, starting from the first end point
Now the y difference in y values must be in the same ratio.
3--4=7
k--4 = k+4
\(\frac{k+4}{7}=\frac{2}{3}\\ 3k+12=14\\ 3k=2\\ k=\frac{2}{3} \)
