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.
Accepted Solution
A:
Answer:[tex]y=1.4x+61[/tex]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 [tex]y=mx+b[/tex], where,m = Slope of line,b = The y-intercept.Let year 1980 be [tex]x=0[/tex]. Now, we have given two points (0,61) and (20, 89).Let us find slope of using coordinates of given points.[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{89-61}{20-0}[/tex][tex]m=\frac{28}{20}[/tex][tex]m=1.4[/tex]Since at [tex]x=0[/tex], [tex]y=61[/tex], so y-intercept is 61.Therefore, the equation [tex]y=1.4x+61[/tex] represents the given equation.