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Question 5022: I'm trying to convert GPA into points (as part of an admissions portfolio). If an applicant has a 4.0 GPA, this would be worth 20 points. A GPA of 3.0 would be worth 12 points; and a GPA of 2.0 would be worth 4 points. Please help determine the slope of the line and the constant (so we can assign points to students with a range of GPA from 0 to 4.0)
points = m(GPA) + b
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Let's start by listing some ordered pairs from the given data:
The oredered pairs will consist of the GPA as the abscissa (the x-value) and the number of points as the ordinate (the y-value). (GPA, Points)
(4, 20)
(3, 12)
(2, 4)
From these ordred pairs we can calculate the slope, m, of the line represented by the linear function: P = m(GPA) + b Use the first two ordered pairs.
m = (y2-y1)/(x2-x1)
m = (12-20)/3-4)
m = -8/-1
m = 8 The slope is 8.
Now we can calculate the contant term, b, using P = 8(GPA) + b, by substituting the P (# of points) and the corresponding GPA from the list of data. Using the first data pair (although any corresponding pair from the list could just as well be used).
20 = 8(4) + b
20 = 32 + b
b = -12
Now we can write the final equation: P = 8(GPA) - 12
The verification is left as an exercise for the student.
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