Question

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

y=9900x−200

Answer 1

To find the equation of the line which represents the population change over time, we need to first determine the slope of the line (change in population per year) and then use the point-slope form of a linear equation.

We are given two points based on the population at different times:

1. In 2013 (which is 3 years from 2010), the population is 9,300.
2. In 2019 (which is 9 years from 2010), the population is 8,100.

We can denote these points as follows:

• Point 1 (x₁, y₁): (3, 9300)
• Point 2 (x₂, y₂): (9, 8100)

Now, we can calculate the slope \( m \) of the line using the formula:

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

Plugging in the values:

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

Next, we can use the slope-intercept form of a line, which is:

\[ y = mx + b \]

We have found that the slope \( m = -200 \). Now we can use one of the points to find the y-intercept \( b \). Let's use point (3, 9300):

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

Calculating this gives:

\[ 9300 = -600 + b \] \[ b = 9300 + 600 = 9900 \]

Now we have both the slope and the y-intercept:

The equation of the line is:

\[ y = -200x + 9900 \]

Thus, the correct answer is:

y = -200x + 9900