The slope-intercept form:

The formula of a slope:

We have the points (-4, 47) and (2, -16). Substitute:

Therefore we have:

Put the coordinates of the point (2, -16) to the equation:

Answer: 
Answer:
k=-1827/685
Step-by-step explanation:
8/9k+9/5=-4-9/7k
8/9k-(-9/7k)=-4-9/5
8/9k+9/7k=-20/5-9/5
56/63k+81/63k=-29/5
137/63k=-29/5
k=(-29/5)/(137/63)
k=(-29/5)(63/137)
k=-1827/685
I don't know what method is referred to in "section 4.3", but I'll suppose it's reduction of order and use that to find the exact solution. Take

, so that

and we're left with the ODE linear in

:

Now suppose

has a power series expansion



Then the ODE can be written as


![\displaystyle\sum_{n\ge2}\bigg[n(n-1)a_n-(n-1)a_{n-1}\bigg]x^{n-2}=0](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Csum_%7Bn%5Cge2%7D%5Cbigg%5Bn%28n-1%29a_n-%28n-1%29a_%7Bn-1%7D%5Cbigg%5Dx%5E%7Bn-2%7D%3D0)
All the coefficients of the series vanish, and setting

in the power series forms for

and

tell us that

and

, so we get the recurrence

We can solve explicitly for

quite easily:

and so on. Continuing in this way we end up with

so that the solution to the ODE is

We also require the solution to satisfy

, which we can do easily by adding and subtracting a constant as needed:
Are you asking for a place or the population?