Starting salaries in the United States for associates with master's degrees in financial engineering (FE) have been rising approximately linearly, from $74,800 in 2009 to $89,800 in 2013.†(a)Use the two (year, salary) data points (0, 74.8) and (4, 89.8) to find the linear relationship y = mx + b between x = years since 2009 and y = salary in thousands of dollars.y = 3.75x+74.8 (b)Use your formula to predict a new FE associate's salary (in dollars) in 2038. [Hint: Since x is years after 2009, what x-value corresponds to 2038?] (Round your answer to the nearest dollar.)

(a) To find the linear relationship between x = years since 2009 and y = salary in thousands of dollars, we can use the formula y = mx + b, where m is the slope of the line and b is the y-intercept.

First, we need to find the slope (m). The slope is the change in y divided by the change in x. In this case, the change in y (salary) is $89.8k -$74.8k = $15k. The change in x (years) is 4 years - 0 years = 4 years. So, the slope (m) is$15k / 4 years = $3.75k/year.

Next, we need to find the y-intercept (b). This is the value of y when x = 0. In this case, when x (years since 2009) is 0, y (salary) is $74.8k. So, b =$74.8k.

Therefore, the linear relationship is y = 3.75x + 74.8.

(b) To predict a new FE associate's salary in 2038, we need to find the x-value that corresponds to 2038. Since x is years after 2009, the x-value for 2038 is 2038 - 2009 = 29 years.

Substituting x = 29 into the equation y = 3.75x + 74.8, we get y = 3.75 * 29 + 74.8 = $184.25k.

So, the predicted salary for a new FE associate in 2038 is $184,250 (rounded to the nearest dollar).