Question

In 2011, the Miami Marlins had about 11,000 followers on a social media site. In 2016, they had about 240,000 followers. Which equation represents the number of followers y the Miami Marlin’s had x years after they joined the site in 2009?

Answer 1

The equation representing the number of followers y the Miami Marlins had x years after they joined the site in 2009 is y = 45,800x - 80,600, where x is the number of years since 2009.

Step-by-step explanation:

To determine the equation representing the number of followers y the Miami Marlins had x years after they joined the social media site in 2009, we can use two data points provided. In 2011 (2 years after joining), they had about 11,000 followers, and in 2016 (7 years after joining), they had about 240,000 followers.

Let's denote the year they joined as year 0, the starting year. Then the two points we can use are (2, 11,000) and (7, 240,000). You can find the slope (m) of the equation, which represents the rate of change of followers per year, using the formula m = (y2 - y1) / (x2 - x1).

1. Find the slope: m = (240,000 - 11,000) / (7 - 2) = 229,000 / 5 = 45,800
2. Write the equation using the slope-intercept form y = mx + b. We know that when x = 0 (in 2009), y should be 0 because that's when the account was created. We also have the point (2, 11,000), which we can use to solve for b, the y-intercept.
3. Substitute the point into the slope-intercept equation: 11,000 = 45,800(2) + b, which gives us b = 11,000 - 91,600 = -80,600
4. Therefore, the equation representing the number of followers is y = 45,800x - 80,600

This linear equation models the growth of the Miami Marlins' social media followers from the point they joined the site in 2009.