Question

Please help due today i beg of u no one would help me .......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:

The linear function to model the relationship between the number of hours worked and the money earned is y = 35 x + 200

Part B:

The meaning of slope in the text context of the problem is his hourly rate each month (he earns $35 per hour each month)

Step-by-step explanation:

The form of the linear function is f(x) = m x + b, where

• m is the slope (the rate of change)
• b is the y-intercept (value y at x = 0)

∵ 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

- Let f(x) represents his earning each month and x represents

  the number of hours he works

∴ f(x) = m x + b, where m is the his earning per hour and b is

   the fixed amount he earning each month

∵ When he works 55 hours during the month, he earns $2,125

∴ f(x) = 2125 at x = 55

- Substitute them in the function above

∴ 2125 = m(55) + b

∴ 55m + b = 2125 ⇒ (1)

When he works 30 hours during the month, he earns $1,250

∴ f(x) = 1250 at x = 30

- Substitute them in the function above

∴ 1250 = m(30) + b

∴ 30m + b = 1250 ⇒ (2)

Now we have a system of equations to solve it

Subtract equation (2) from equation (1) to eliminate b

∴ 25m = 875

- Divide both sides by 25

∴ m = 35

- Substitute the value of m in equation (2) to find b

∵ 30(35) + b = 1250

∴ 1050 + b = 1250

- Subtract 1050 from both sides

∴ b = 200

∴ y = 35 x + 200

Part A:

The linear function to model the relationship between the number of hours worked and the money earned is y = 35 x + 200

∵ m is the rate of change in his earning according to his

   working hours

∵ m = 35

∴ He earns $35 per hour

Part B:

The meaning of slope in the text context of the problem is his hourly rate each month (he earns $35 per hour each month)

Learn more:

You can learn more about the system of equations in brainly.com/question/3739260

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