Determine a linear function that will convert 285 to 200

Mathematics
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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 and 60. A) Determine a linear function that will convert 285 to 200

Sep 9th, 2014

Linear function: y = m x + b

y= f(285)=200

y= f(75)=60

m = dif y/ dif x = (200-60)/(285-75) = 140/210 = 2/3

y = 2/3 x + b

To find b you can use the point (75,60)

2/3 (75) + b = 60

50 + b = 60

         b = 10

Answer: The function is: y = 2/3 x + 10

Checking:

(285, 200) --- 2/3 (285) + 10 = 190 + 10 = 200

(75,60) --- 2/3 (75) + 10 = 50 + 10 = 60

Sep 11th, 2014

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