Question

A computer technician keeps track of his earning through tout each months. The technician observes that his earnings are a linear function of the number of house he works during the month. The technician finds that when he works 55 hours during the month, he earns $2,125 and when he works 30 hours, he earns $1,250

Part A- write a linear function to model the relationship between the number of hours worked and the money earned





Part B- explain the meaning of slope in the text context of the problem

Answer 1

Part A : E = 35h + 200

Part B : The per hour charges of the technician is $35/hour.

Explanation:

The technician observes that his earnings are a linear function of the number of hours he works during the month. The technician finds that when he works 55 hours during the month, he earns $2,125 and when he works 30 hours, he earns $1,250 .

If we consider the number of hours that he works in a month is h and the amount he earns in dollars is E, then (30,1250) and (55,2125) are the two ordered pairs.

Part A : Therefore, the linear function to model the relationship between the number of hours worked and the money earned will be

`(E - 2125)/(2125 - 1250) = (h - 55)/(55 - 30)`

⇒ E - 2125 = 35(h - 55)

⇒ E - 2125 = 35h - 1925

⇒ E = 35h + 200

Part B : The equation above is in the slope-intercept form and the slope is 35 which means that the per hour charge of the technician is $35/hour. (Answer)