algabra word problem

Question

The population of the Wallingfried neighborhood has been growing steadily since 1984. In 1989, the population was 38500 people. In 1998, it was 44800 people. Find an equation in the form y=mx+b, where x is the number of years past 1984 and y is the population of Wallingfried.

Answer 1

To solve this problem, you must find the rate of population growth or the slope, and the y-intercept or the population of Wallingfried in 1984. Using the y₂-y₁ /x₂-x₁ formula for calculating slope and plugging in the given values for (x₁,y₁) and (x₂,y₂), the slope for this graph can be written as (44,800-38,500) / (14-5) which simplifies to a slope of 700. From here, you can use the slope to find the value of the y-intercept a few different ways: 1.- Plug the slope and given values for (x₁,y₁) or (x₂,y₂) into the y=mx+b equation to solve for b. OR 2.- multiply the slope by 5 years and subtract this number from the population in 1989 to find the population in 1984. Both methods should give you a value of 35,000 for the population in 1984. After substituting in the slope and intercept values in the y=mx+b equation you get the function y=700x+35000 which can be graphed to represent the population growth in the Wallingfried neighborhood since 1984.