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.

Question

A coordinate plane showing Newspaper Circulation, Years Since 2000 on the x-axis and Circulation on the y-axis. A line starting at (0, 80,000), passing through a point at (10, 50,000) and ending at (18, 25,000).

What number will complete the point-slope equation that models this scenario?

y−50,000=[_______](x−10)

−3,000
−2,000
2,000
3,000

Answer 1

To determine the number that will complete the point-slope equation for this scenario, we first need to find the slope of the line that models the newspaper circulation over the years.

We have two points from the information given in the problem:

1. The year 2000 (x = 0): (0, 80,000)
2. The year 2010 (x = 10): (10, 50,000)

The slope \( m \) is calculated using the formula:

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

Substituting our points into this formula:

\[ m = \frac{50,000 - 80,000}{10 - 0} = \frac{-30,000}{10} = -3,000 \]

So, the slope of the line is -3,000.

Now we can use this slope to complete the point-slope equation:

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

Here, we can use the point (10, 50,000):

• \( y_1 = 50,000 \)
• \( x_1 = 10 \)
• \( m = -3,000 \)

Substituting these values into the point-slope equation, we get:

\[ y - 50,000 = -3,000(x - 10) \]

Therefore, the number that completes the point-slope equation is −3,000.