Write an equation in point-slope form to represent the situation. Assume a linear relationship between the given quantities.
In 1998, the deer population of a certain area was 1200. In 2006, the population was 2000.
To write an equation in point-slope form to represent the given situation, we need to determine the slope and a point on the line.
Let's start by finding the slope. The slope represents the rate of change between the two given points, which in this case are the years 1998 and 2006.
The change in the deer population is calculated by subtracting the initial population from the final population:
Change in population = Final population - Initial population = 2000 - 1200 = 800.
The change in years is calculated by subtracting the initial year from the final year:
Change in years = Final year - Initial year = 2006 - 1998 = 8.
Now, we can find the slope by dividing the change in population by the change in years:
Slope = Change in population / Change in years = 800 / 8 = 100.
Next, let's choose a point on the line. We can use either the initial or final data point.
Using the initial data point from 1998 (1200 deer population), our point is (x1, y1) = (1998, 1200).
Finally, we can write the equation in point-slope form. The point-slope form equation is given by:
y - y1 = m (x - x1),
where m is the slope and (x1, y1) is a point on the line.
Plugging in the values, we get:
y - 1200 = 100 (x - 1998).
This equation, y - 1200 = 100 (x - 1998), represents the linear relationship between the years and the deer population in point-slope form.