A computer technician keeps track of his earnings throughout each month. 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 earn $2,125 and when he works 30 hours, he earns $585
Part A: Write a linear function to model the relationship between the number of hours worked and the money earned.
Function _____________
Part B: Explain the meaning of slope in the context of the problem.
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by working 25 extra hours, he earned $1540 more. That's $61.60/hr
So, his pay for x sours is
p(x) = 61.6x-1263
the slope is the rate of change ($ per hour), or his hourly rate.
Where did you get 1263 from>?
yea whered you get 1263 from?
Plug the slope of 61.6, y of 585 and an x of 30 to get the y-intercept of -1263 which is b. So your formula would be y = 61.6x - 1263 for this problem.
Part A: To write a linear function to model the relationship between the number of hours worked and the money earned, we need to find the equation of a line.
First, let's identify the variables:
- The number of hours worked will be represented by "h"
- The earnings will be represented by "e"
We have two data points:
- When the technician works 55 hours, he earns $2,125 (h = 55, e = 2125)
- When the technician works 30 hours, he earns $585 (h = 30, e = 585)
Now, we can find the slope (m) using the formula:
m = (e2 - e1) / (h2 - h1)
Using the given data points:
m = (585 - 2125) / (30 - 55)
m = (-1540) / (-25)
m = 61.6
The slope (m) represents the rate at which the earnings change per hour worked.
Next, we can use the slope-intercept form of a linear equation, y = mx + b, to find the y-intercept (b).
We can take any of the two data points to substitute the values and solve for b. Let's use the point (h = 55, e = 2125).
2125 = 61.6(55) + b
2125 = 3386 + b
b = 2125 - 3386
b = -1261
Now we have the slope (m) and the y-intercept (b), we can write the linear function:
e = 61.6h - 1261
Part B: The slope of the linear function represents the rate of change in earnings with respect to the number of hours worked. In this problem, the slope of 61.6 means that for every additional hour worked, the technician's earnings increase by $61.6.
So, in the context of the problem, the slope tells us the amount of money the technician earns for each additional hour worked.