Question

The population of a town was taken in 2010. After 3 years, the population of the town is 9,300. After 9 years, the population of the town is 8,100. Assuming the change in population is constant each year, which is the equation of the line? (1 point) Responses y=−200x+9900 y is equal to negative 200 x plus 9900 y=9900x−200 y is equal to 9900 x minus 200 y=200x+9900 y is equal to 200 x plus 9900 y=−200x+9300

Answer 1

To find the equation of the line that represents the population of the town over time, we can use the two given data points:

1. After 3 years (2013), the population is 9,300.
2. After 9 years (2019), the population is 8,100.

Let's denote:

• \( x \) as the number of years since 2010.
• \( y \) as the population.

The points we have are:

• \( (3, 9300) \)
• \( (9, 8100) \)

To find the slope \( m \) of the line, we use the formula: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Substituting our points: \[ m = \frac{8100 - 9300}{9 - 3} = \frac{-1200}{6} = -200 \]

Now we use the point-slope form of a line, \( y - y_1 = m(x - x_1) \). We can use one of the points, say \( (3, 9300) \):

\[ y - 9300 = -200(x - 3) \]

Expanding this: \[ y - 9300 = -200x + 600 \] \[ y = -200x + 9900 \]

Therefore, the equation of the line is: \[ \boxed{y = -200x + 9900} \]