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

### Question Description

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.

## Explanation & Answer

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

Gradient = 200-60/285-75

=140/210

=2/3

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

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