Find a linear fn. that will convert 285 to 200 & 75 to 60

Question Description

I’m stuck on a Mathematics question and need an explanation.

The highest and lowest marks awarded on an examination were 285 and 75. All the marks must be reduced so that the highest and lowest marks become 200 & 60. Determine a linear function that will convert 285 to 200 and 75 to 60.

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Final Answer

The required line will pass through (285, 200) and (75, 60)

Gradient = 200-60/285-75



Required equation is (y- y1) =m (x-x1)

                                  (y-60) =2/3 (x-75)

                        y-60 =2/3x-50

                       y = 2/3x +10   (this is best for conversion – y is the adjusted score, x the raw mark)

or                   2x-3y +10 = 0

John Si. (970)
UT Austin

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