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.

Question

Assuming the change in population is constant each year, which is the equation of the line?

(1 point)
Responses

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

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

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

y=−200x+9900
𝑦
=
−
200

Answer 1

To find the equation of the line that models the population over time, we first need to identify the points on the graph:

1. The population at the end of 2013 (3 years after 2010) is 9,300. This gives us the point (3, 9300).
2. The population at the end of 2019 (9 years after 2010) is 8,100. This gives us the point (9, 8100).

Next, we can find the slope \( m \) of the line using the formula:

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

Substituting the points (3, 9300) and (9, 8100):

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

Now that we have the slope \( m = -200 \), we can use point-slope form to find the equation of the line. We can use one of the points, for instance (3, 9300).

The point-slope form is:

\[ y - y_1 = m(x - x_1) \]

Substituting \( m = -200 \), \( x_1 = 3 \), and \( y_1 = 9300 \):

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

Expanding this equation:

\[ y - 9300 = -200x + 600 \]

\[ y = -200x + 9900 \]

Thus, the equation of the line that models the population over time is:

\[ y = -200x + 9900 \]

So the correct response is:

y = −200x + 9900