Jonah collects rainwater in a large barrel that weighs 30 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 113.4 pounds. When there are 20 gallons of water, the total weight is 196.8 pounds. Which equation and graph match this situation? A. y = 8.34x + 30 B. y = 30x + 8.34 C. y = 30x + 8.34 D. y = 8.34x + 30

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05-06-2018
Mathematics

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Jonah collects rainwater in a large barrel that weighs 30 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 113.4 pounds. When there are 20 gallons of water, the total weight is 196.8 pounds. Which equation and graph match this situation? A. y = 8.34x + 30 B. y = 30x + 8.34 C. y = 30x + 8.34 D. y = 8.34x + 30

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carlosego carlosego · Answer 1 · 2018-06-14T19:04:08+02:00

The first thing we are going to do for this case is define variables.
We have then:
x: number of gallons of water
y: total weight
We then have an equation of the form:
[tex]y-yo = m (x - xo) [/tex]
Where,
[tex]m = (y2 - y1) / (x2 - x1) [/tex]
Substituting values:
[tex]m = (196.8 - 113.4) / (20 - 10) m = 8.34[/tex]
We choose an ordered pair:
[tex](xo, yo) = (10, 113.4) [/tex]
Substituting values:
[tex]y-113.4 = 8.34 (x - 10) [/tex]
Rewriting:
[tex]y = 8.34x - 83.4 + 113.4 y = 8.34x + 30[/tex]
Answer:
y = 8.34x + 30