In 1997, a typical American consumed 52 liters of bottled water, and in 2001, a typical

American consumed 74 liters of bottled water. Let y be the number of liters of bottled water
consumed by a typical American in the year x, where x = 0 represents the year 1997.
(a) Which of the following linear equations could be used to predict the number of liters of
bottled water consumed in a given year x, where x = 0 represents the year 1997? Explain/show
work.

A. y = 22x + 52
B. y = 5.5x + 52
C. y = −5.5x + 74
D. y = 22x − 6


(b) Use the equation from part (a) to estimate the number of liters of bottled water consumed by
a typical American in 2009. Show work.

(c) Fill in the blanks to interpret the slope of the equation: The average rate of change of bottled
water consumed with respect to time is ______________________ per ______________.
(Include units of measurement.)

started at 52, increased 22 in 4 years, or 5.5 per year.

Looks like B to me.

Now use that formula to answer the other parts.

(a) To find the linear equation that could be used to predict the number of liters of bottled water consumed in a given year x, where x = 0 represents the year 1997, we need to first find the slope (m) and the y-intercept (b) using the given data points (0, 52) and (4, 74).

The slope (m) of a linear equation is calculated using the formula:
m = (y2 - y1) / (x2 - x1)

Using the points (0, 52) and (4, 74):
m = (74 - 52) / (4 - 0)
m = 22 / 4
m = 5.5

The y-intercept (b) is the value of y when x = 0. In this case, it's given as 52.

Therefore, the linear equation that could be used to predict the number of liters of bottled water consumed in a given year x is:
y = 5.5x + 52

So, the correct answer is option B.

(b) To estimate the number of liters of bottled water consumed by a typical American in 2009, we need to substitute x = 12 (since 2009 - 1997 = 12) into the equation from part (a).

Plugging in x = 12:
y = 5.5 * 12 + 52
y = 66 + 52
y = 118

Therefore, the estimated number of liters of bottled water consumed by a typical American in 2009 is 118.

(c) The slope of the equation represents the average rate of change of bottled water consumed with respect to time. In this case, the slope is 5.5, which means that on average, the number of liters of bottled water consumed by a typical American increases by 5.5 units per year.

So, the interpretation of the slope is: The average rate of change of bottled water consumed with respect to time is 5.5 liters per year.