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

Answer:

$y = 320x +2080$

Step-by-step 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)

$m = \frac{y_2 - y_1}{x_2 - x_1}$

$m = \frac{4000 - 2400}{6 - 1}$

$m = \frac{1600}{5}$

$m = 320$

Next, we calculate the line equation as follows:

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

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

$y - 2400 = 320x - 320$

$y = 320x - 320 + 2400$

$y = 320x +2080$