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.