# Math

The tops of seven water fountains in the Italian City of Reggio Emilia form a straight line. The first fountain is 120cm and the last one is 12cm. How tall is the third water fountain from the left?

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1. Use Cartesian geometry
let the first be at (1,120) and the last one at (7,12)
slope = (120-12)/(1-7) = -18

so for each increase in x, the height drops 18 cm
so you want two decreases,
height of third = 120-2(18) = 84

or
find the equation:
y = -18x + b
at (7,12)
12 = -18(7) + b
b = 138

y = -18x + 138
so when x = 3
y = -18(3) + 138 = 84 cm

or

the fountains would be at
(1,120) , (2, 102) , (3,84) , (4,66) , (5,48) , (6, 30), (7, 12)

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posted by Reiny
2. Thank you

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