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 200 x plus 9900 y=−200x+9300 y is equal to negative 200 x plus 9300 y=9900x−200 y is equal to 9900 x minus 200 y=−200x+9900

Answer 1

To determine the equation of the line representing the population of the town, we need to find the slope and y-intercept based on the given population data.

We have two points:

1. At \(t = 3\), the population \(y = 9300\).
2. At \(t = 9\), the population \(y = 8100\).

We can express these points as:

• Point 1: \((3, 9300)\)
• Point 2: \((9, 8100)\)

Step 1: Calculate the slope (m)

The formula for the slope \(m\) between the two points is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Substituting the points: \[ m = \frac{8100 - 9300}{9 - 3} = \frac{-1200}{6} = -200 \]

Step 2: Use the point-slope form to find the equation

Now we can use point-slope form to find the equation. We can use point 1 \((3, 9300)\): \[ y - y_1 = m(x - x_1) \] Substituting: \[ y - 9300 = -200(x - 3) \]

Step 3: Simplify the equation

Distributing and rearranging: \[ y - 9300 = -200x + 600 \] \[ y = -200x + 600 + 9300 \] \[ y = -200x + 9900 \]

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