The population of the Wallingfried neighborhood h

Question

The population of the Wallingfried neighborhood has been growing steadily since 1981. In 1987, the population was 35200 people. In 1992, it was 43700 people.

Find an equation in the form y = m x + b, where x is the number of years past 1981 and y is the population of Wallingfried.

Answer 1

Since we have been given two years with their populations, we actually have two points.  The points are (6,35,200) and (11,43,700).

The first step to find the equation of the line is finding the slope.  The slope formula says:

m = (y₂ - y₁)/(x₂ - x₁)

After substituting, we have

m = (43,700 - 35,200)/(11 - 6)

m = 8,500/5

m = 1,700

Now that we have the slope, we can use the point-slope formula to do this.  I will use the first point, but you will get the same answer if you use the second point.

y - y₁ = m(x - x₁)                                               Point-slope formula

y - 35,200 = 1,700(x - 6)                                    Substitution

y - 35,200 = 1,700x - 10,200                               Distribute the 1,700

y -35,200 + 35,200 = 1,700x - 10,200 + 35,200    Add 35,200 to each side

y = 1,700x + 25,000                                           Simplify