Question

According to a​ census, there were 61 people per square mile​ (this is called the population​ density) in a certain country in 1980. By​ 2000, the number of people per square mile had grown to 89 . Use this information to develop a linear equation in​ slope-intercept form. In developing the​ equation, think of 1980 as year zero. Let x be the time in years and let y be the population density. Write a linear equation in​ slope-intercept form to model the given information.

Answer 1

`y=1.4x+61`

Explanation:

Let x be the time in years and let y be the population density.

We know that slope-intercept form of an equation is in format
`y=mx+b`, where,

m = Slope of line,

b = The y-intercept.

Let year 1980 be
`x=0`. Now, we have given two points (0,61) and (20, 89).

Let us find slope of using coordinates of given points.

`m=(y_2-y_1)/(x_2-x_1)`

`m=(89-61)/(20-0)`

`m=(28)/(20)`

`m=1.4`

Since at
`x=0`,
`y=61`, so y-intercept is 61.

Therefore, the equation
`y=1.4x+61` represents the given equation.