I believe, the line graph of population refers to the graph of growth of total human population over time.
Though there are some dissenting voice, there is general consensus among economists and other experts on human welfare about the need to keep the human population constant. Thus an ideal graph of population wit time shown on x-axis and population on y-axis will be a horizontal straight line.
If left entirely to the bounty of nature, without the aid of technology, the earth has a limited capacity in terms of the size of population it can support. In nature when the population of any species of animal increase beyond the capacity of a piece of land to support that population is restricted by nature itself. However, technological development have given the humans to support ever increasing population on the earth, simultaneously increasing their standard of living also. The technology, particularly that related to medical science, also gave humans the power to increase their population beyond capacity of the earthly resources to support them at levels of prosperity they aspire to, and perhaps have a right to. IN light of this the only sensible means of giving all the humans a kind of life they have a right to is by preventing further growth of population.
I am not going to the extreme of suggesting the alternative of actually trying to reduce the population by restricting birth rate further, because this will create additional problem of the age composition. Reduction in population in this way can not be achieved without passing through a stage where for a long period the population will be composed of very large proportion of very old people, supported by very small proportion of adults for carrying out the production activities. This can pose serious economic and sociological problems.