Question

19. 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

The linear equation in slope intercept form for population of Jose's town is y = 320x + 2400.

Solution:

Given, 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.  

We have to write a linear equation, in slope- intercept form, that represents this data.

Now, let the change in population per year be p.

Then, population in a year = population change per year $\times$ number of years + population in 1995.

⇒population in a year = p$\times$ x + population in 1995

⇒ population in a year = p $\times$ x + 2400

Here we have an case that, population in 2000 is 4000  

Then, number of years since 1995 = 5  

So, 4000 = p $\times$ 5 + 2400 ⇒ 5p = 4000 – 2400 ⇒ 5p = 1600 ⇒ p = 320

Then, our equation will be population in a year = 320x + 2400  

Considering the population in a year as y ⇒ y = 320x + 2400.

Hence, the linear equation in slope intercept form is y = 320x + 2400.