Question

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​

Answer 1

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

Explanation:

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

• m is the slope (rate of change)

• b is the y-intercept (initial value)

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

• Δy is the change of y

• Δx is the change of x

∵ 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 =
`(83.4)/(10)`

∴ 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