Answer :
Answer:
[tex]y=320x+2400[/tex]
Step-by-step explanation:
Remember, a line has the form [tex]y=mx+b[/tex], where [tex]m[/tex] is the slope and [tex]b[/tex] is the y-intercept. In this cases, y represents the population when have been passed x years since 1995.
Since x represent the number of years since 1995, then in 1995, x=0 and the population is 2400. Then a point of the linear equation is (x,y)=(0,2400).
In 2000 has been passes 5 years since 1995 and the population is 4000, this means that x=5 and y=4000. Then other point in the line is (x,y)=(5,4000)
For find the equation of the line that describe the preview situation we use the points found.
Remember, if [tex](x_1, y_1)[/tex] and [tex](x_2,y_2)[/tex] are pointsin the plane, the slope of the line that passes through the points is
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex], and the line is of the form [tex]y-y_1=m(x-x_1)[/tex]
Then, using the points (0,2400),(5,4000), we have that
[tex]m=\frac{4000-2400}{5-0}=\frac{1600}{5}=320[/tex]
and [tex]y-2400=320(x-0)\\y-2400=320x\\y=320x+2400[/tex]