According to a study, the relation between the average annual earnings of males and females with various levels of educational attainment can be modeled by the function F = 0.78M - 1.315

where M and F represent the average annual earnings (in thousands of dollars) of males and females, respectively. (a) Viewing F as a function of M, what is the slope of the graph of this function? (b) what is M?

(c) When the average annual earnings for males reach $65,000, what does the equation predict for the average annual earnings for females?

a) m = 0.78

b) Average annual earnings by Males

c) F = $ 30,548.685

Step-by-step explanation:

Given:

- The relationship between the average annual earning of Females F is expressed as a function of earnings by males M as:

F = 0.78*M - 1.315

Find:

(a) Viewing F as a function of M, what is the slope of the graph of this function?

(b) what is M?

(c) When the average annual earnings for males reach $65,000, what does the equation predict for the average annual earnings for females?

Solution:

a)

- The given expression can be compared with a linear equation of the form:

y = m*x + c

Where,

y is the dependent variable

m is the slope of the graph

x is the independent variable

c is the intercept when x = 0

- So for our case, y = F, m = 0.78, x = M, c = - 1.315

b)

- The variable M is the independent variable with the domain [ 0, infinity ] denotes the average annual earnings of Males in dollars ($).

c)

- When average annual earnings by males is $ 65,000 i. e M = 65,000, We compute F by the given expression:

F = 0.47 * 65,000 - 1.315

F = $ 30,548.685

- The average annual earning by females is $ 30,549 when earning by males reach $65,000.