Question

the newspaper in haventown had a circulation of 80,000 papers in the year 2000. in 2010, the circulation was 50,000. with x=0 representing the year 2000, the graph below models this scenario.
newspaper circulation
(graph: x-axis: years since 2000, y-axis: circulation. point (10, 50000) marked, line from (0,80000) to (18, ~25000))
what number will complete the point - slope equation that models this scenario?
y - 50,000 = ______(x - 10)
options: -3,000; -2,000; 2,000; 3,000

Explanation:

Step1: Identify two points

We have two points: when \( x = 0 \) (year 2000), \( y = 80000 \); when \( x = 10 \) (year 2010), \( y = 50000 \).

Step2: Calculate the slope

The slope \( m \) is given by the formula \( m=\frac{y_2 - y_1}{x_2 - x_1} \). Substituting the points \((0, 80000)\) and \((10, 50000)\), we get \( m=\frac{50000 - 80000}{10 - 0}=\frac{- 30000}{10}=-3000 \).
The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \((x_1,y_1)=(10,50000)\) and \( m=-3000 \). So the number in the blank is \(-3000\).

Answer:

-3,000