Question

The population of Garden City in 1995 was 2,400. In 200, the population was 4,000. Write a linear equation in slope-intercept form that represents this data.

Answer 1

`y = 320x +2080`

Explanation:

Given

Population in 1995 = 2400

Population in 2000 = 4000

Required

Determine the linear equation

Let the years be represented with x.

In 1995, x = 1 i.e. the first year

In 2000, x = 6

Let y represents the population

When x = 1; y = 2400

When x = 6; y = 4000

First, we calculate the slope (m)

`m = (y_2 - y_1)/(x_2 - x_1)`

`m = (4000 - 2400)/(6 - 1)`

`m = (1600)/(5)`

`m = 320`

Next, we calculate the line equation as follows:

`y - y_1 = m(x - x_1)`

`y - 2400 = 320(x - 1)`

`y - 2400 = 320x - 320`

`y = 320x - 320 + 2400`

`y = 320x +2080`