Question

Ivy collects rainwater in a large barrel that weighs 35 pounds. When there are 10 gallons of water in the barrel, the total weight of the barrel and the water is 118.4 pounds. When there are 20 gallons of water, the total weight is 201.8 pounds which equation and graph match this situation?

Answer 1

y = 8.34x + 35

Explanation:

Ivy has an empty barrel having weight = 35 pounds

Having 10 gallons of water barrel weighs = 118.4 pounds

After collecting 20 gallons of water barrel weighs = 201.8 pounds

There is a common difference in the weight of the barrel as he collects the rain water = (201.8 - 118.4) = 83.4 pounds

Therefore, its a linear process and forms a straight line when we graph the function.

Let the equation of the line is,

y = mx + b

Where m = slope of the line

b = y-intercept

Two points lying on the line will be (0, 35) and (10, 118.4)

Slope of the line 'm' =
`(y_(2)-y_(1))/(x_(2)-x_(1))`

=
`(118.4-35)/(10-0)`

= 8.34

y-intercept of the line 'b' = 35

Therefore, equation of the line is,

y = 8.34x + 35