Mrs. Bailey gives a test, and her students’ scores range from 30 to 70. She decides to curve the scores, so that they range from 65 to 95. Let "x" be an original score, and "y" be a curved score. Using the ordered pairs (30,65) and (70,95), write the equation in slope/intercept form that she should use to curve the test scores.

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MechEngineer MechEngineer · Answer 1 · 2019-12-18T10:57:18+01:00

Answer:

f(x) = x*3/4 + 42.5

Step-by-step explanation:

The original difference between the pair is 70 - 30 = 40

The new difference between the pair is 95 - 65 = 30

Since the differences are not the same, Mrs Bailey must first perform a (slope) multiplication by a factor of 30/40 or 3/4

Then 30 * 3/4 = 22.5

Then she can shift the scores up by 65 - 22.5 = 42.5 in order to get the range from 65 to 95

Therefore, f(x) = x*3/4 + 42.5. We can test that

f(30) = 30*3/4 + 42.5 = 65

f(70) = 70*3/4 + 42.5 = 95