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.

a) y = 800x + 2400
b) y = 800x + 4000
c) y = 400x + 2400
d) y = 400x + 4000

Answer 1

To create a linear equation in slope-intercept form that represents the population growth from 2400 in 1995 to 4000 in 2000, calculate the slope and use the starting population as the y-intercept. The correct equation is y = 320x + 2400.

Step-by-step explanation:

The question asks for a linear equation in slope-intercept form representing the population growth of a town from 1995 to 2000.

We know the population was 2400 in 1995 and 4000 in 2000. We let x represent the number of years since 1995. The slope (m) of the line is the change in population divided by the change in time. Therefore, m = (4000 - 2400) / (2000 - 1995) = 1600 / 5 = 320. The y-intercept (b) is the population at x = 0, which is the year 1995, so b = 2400. The equation of the line is y = 320x + 2400.