SOLUTION: Normally, the longer you work for a company, the higher your salary per hour. Hector surveyed the people at his company and placed his data in the table below. (Please, pretend

Question 415684: Normally, the longer you work for a company, the higher your salary per hour. Hector surveyed the people at his company and placed his data in the table below.
(Please, pretend it's a table.)
Number of Years at Company- 1, 3, 6, 7
Salary per hour-$7, $8.50, $10.75, $11.50
a.Use Hector's data to estimate how much he makes, assuming he has worked at the company for 12 years.
b.Hector is hiring a new employee who will work 20 hours a week. How much should the new employee earn for the first week?
Answer by htmentor(1343) (Show Source): You can put this solution on YOUR website!
This table represents (x,y) pairs on a line
(1,7)
(3,8.50)
(6,10.75)
(7,11.50)
The slope of the line is given by m=(y2-y1)/(x2-x1) -> (8.5-7)/(3-1) -> m=0.75
So y = 0.75x + b, or b=y-0.75x
Use any one of the ordered pairs (x1,y1) to solve for b: b=7-0.75(1) -> b=6.25
So the equation which determines the salary is y=0.75*x+6.25
To solve a. we substitute x=12 in the above equation: y=0.75*12+6.25
So the salary per hour after 12 years = 9+6.25=$15.25
For a new employee, x=0 years -> y=6.25
So the answer to b. is 20*$6.25 = $125
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