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=9900x−200
y is equal to 9900 x minus 200

y=200x+9900
y is equal to 200 x plus 9900

y=−200x+9300
y is equal to negative 200 x plus 9300

y=−200x+9900

Answer 1

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

- At \( x = 3 \) (which corresponds to the year 2013), the population \( y = 9300 \).
- At \( x = 9 \) (which corresponds to the year 2019), the population \( y = 8100 \).

First, we need to calculate the slope \( m \) of the line using the formula:

\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]

Using our points:
- \( (x_1, y_1) = (3, 9300) \)
- \( (x_2, y_2) = (9, 8100) \)

Plugging in the values:

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

Next, we can use one of the points to find the equation of the line in slope-intercept form \( y = mx + b \). Using point \( (3, 9300) \):

\[
y = -200x + b
\]

To find \( b \), substitute \( x = 3 \) and \( y = 9300 \):

\[
9300 = -200(3) + b \\
9300 = -600 + b \\
b = 9300 + 600 \\
b = 9900
\]

Thus, the equation of the line is:

\[
y = -200x + 9900
\]

The correct response is:

**y=−200x+9900**
y is equal to negative 200 x plus 9900.