Question

The population of Jose’s town in 1995 was 2400 and the population in 2000 was

4000. Let x represent the number of years since 1995. Write a linear equation, in slope-

intercept form, that represents this data.​

Answer 1

`y=320x+2400`

Explanation:

Remember, a line has the form
`y=mx+b`, where
`m` is the slope and
`b` 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
`(x_1, y_1)` and
`(x_2,y_2)` are pointsin the plane, the slope of the line that passes through the points is

`m=(y_2-y_1)/(x_2-x_1)`, and the line is of the form
`y-y_1=m(x-x_1)`

Then, using the points (0,2400),(5,4000), we have that

`m=(4000-2400)/(5-0)=(1600)/(5)=320`

and
`y-2400=320(x-0)\\y-2400=320x\\y=320x+2400`