Lisa collects rainwater in a barrel that weighs 25 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 108.4 pounds. When there are 20 gallons of water, the total weight is 191.8 pounds Which equation matches this situation?

A. y=25x+8.834
B. y=8.34x+25
C. y=25x
D. y=8.34x

The equation that matches this situation is y = 8.34x + 25 ⇒ B

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

The rule of the slope is m = Δy/Δx, where

∵ Lisa collects rainwater in a barrel that weighs 25 pounds

∴ The initial value of the weight is 25 pounds

∴ b = 25

∵ When there are 10 gallons of water in the barrel, the total weight

  of the barrel and the water is 108.4 pounds

∴ At x = 10, y = 108.4

∵ When there are 20 gallons of water, the total weight is 191.8 pounds

∴ At x = 20, y = 191.8

→ Find Δx and Δy

∵ Δx = 20 - 10 = 10

∵ Δy = 191.8 - 108.4 = 83.4

→ Substitute them in the rule of the slope above

∴ m =

∴ m = 8.34

→ Substitute the values of m and b in the form of the equation above

∵ y = 8.34x + 25

∴ The equation that matches this situation is y = 8.34x + 25

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