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

Answer:

$y=1.4x+61$

Step-by-step 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.

$m=\frac{y_2-y_1}{x_2-x_1}$

$m=\frac{89-61}{20-0}$

$m=\frac{28}{20}$

$m=1.4$

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

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