Final answer:
To express the median family incomes less than a certain amount after x years since 2006, we use the inequality y < 48200 + 1240x. Points (x, y) below this line on a graph are part of the solution set. Upon evaluating, only the point (5, 50000) is part of the solution set, while the others are not.
Step-by-step explanation:
The question involves writing an inequality to represent the median family incomes that are less than a certain amount after x years since 2006 and determining if given points lie in the solution set. To represent the median income as a function of years after 2006, we use the function y = 48200 + 1240x. The inequality to represent annual family incomes y that are less than the median for x years after 2006 would be y < 48200 + 1240x.
To graph this inequality, you plot the line y = 48200 + 1240x and shade the area below the line, which indicates all the income values below the median as it changes each year. When assessing whether given points are part of the solution set, a point (x, y) is part of the solution set if the y-value is less than the median income value at the corresponding x (years after 2006).
- For the point (2, 51000), the median income after 2 years (2008) was y = 48200 + 1240(2) = 50680. 51000 is greater than 50680, so this point is not part of the solution set.
- For the point (8, 69200), the median income after 8 years (2014) was y = 48200 + 1240(8) = 57840. 69200 is greater than 57840, so this point is not part of the solution set.
- For the point (5, 50000), the median income after 5 years (2011) was y = 48200 + 1240(5) = 54000. 50000 is less than 54000, so this point is part of the solution set.
- For the point (10, 61000), the median income after 10 years (2016) was y = 48200 + 1240(10) = 60600. 61000 is greater than 60600, so this point is not part of the solution set.