The average hourly wage y in the U.S. (adjusted for inflation) was exist8.03 in

Question

The average hourly wage y in the U.S. (adjusted for inflation) was exist8.03 in 1970 and exist7.75 in 1998. Let x be the elapsed number of years since 1970 Write a linear function that models this data. Then use the function to find the given value. Y = (simplify your answer and round to T decimal places, including zeros as needed Example: 2 should be written Find the year when the average hourly wage was exist7.87. (Round your answer to Two decimal places, including zeros as needed. Example: 2 should be written as 2.00. Do not include commas.)

Explanation / Answer

When x = 0 the value of Y is 8.03

and when x = 28 the value of Y is 7.75

let the linear relation be

Y = kx+A

the two equations can be formed using the two values of x anf y

8.03=k*0+A or A = 8.03

7.75 = k*28+A

or 28k = 7.75-8.03

or k = (-0.28)/28 = -0.01

so Y = -0.01x+8.03

when Y = 7.87

then 7.87 = -0.01x+8.03

or x = 16

that is its the year 1970+16 = 1986

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