Suppose the maximum healthy weight for a person who is 5 feet 9 inches tall is 1

Question

Suppose the maximum healthy weight for a person who is 5 feet 9 inches tall is 160 pounds, and the maximum healthy weight for someone 6 feet 7 inches tall is 210 pounds. The relationship between weight and height here is linear. (a) Find a linear equation that gives the maximum healthy weight y for a person whose height is x inches over 4 feet 9 inches. (Thus x = 0 corresponds to 4 feet 9 inches and x = 3 to 5 feet.etc.) y = _______ (b) What is the maximum healthy weight for a person whose height is 5 feet? _______ pounds 6 feet? _______ pounds (c) How tall is a person who is at a maximum healthy weight of 240 pounds? _______ feet _______ inches

Explanation / Answer

x = 0 represents 4 feet 9 inches

x = 3 represents 5 feet

so we have two points

( 12 , 160 ) which represents 5 feet 9 inches and 160 pounds

( 22 , 210 ) which represents 6 feet 7 inches and 210 pounds

slope m = (210 - 160 ) / (22- 12 ) = 5

applying point slope form

y - 160 = 5 ( x - 12 )

y = 5x + 100

b) when height is 5 feet

y = 5(3) + 100

y = 115 pounds

when height is 6 feet

plugging x = 15

y = 5(15) + 100

y = 175 pounds

c) plugging y = 240

240 = 5x + 100

5x = 140

x = 28

hence person is 7 feet 1 inches

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