Question

two water tanks are leaking water. the equation and the table each represent the gallons of water in the tank, y, as a function of time in minutes, x. the amount of water in tank a decreases by 11 gallons per minute. the rate of change for tank a is -11. tank a: y = 900 - 11x. tank b: (table with minutes, x: 0,1,2,3 and water in tank (gal), y: 985,975,965,955). find the rate of change for the function that represents tank b. the amount of water in tank b? by? gallons per minute. the rate of change for tank b is?.

Explanation:

Step1: Identify rate of change formula

The rate of change (slope) for a linear function \( y = mx + b \) is \( m \), calculated as \( \frac{\Delta y}{\Delta x} \), where \( \Delta y = y_2 - y_1 \) and \( \Delta x = x_2 - x_1 \).

Step2: Calculate \( \Delta y \) and \( \Delta x \) for Tank B

Using table values (e.g., \( x_1 = 0, y_1 = 985 \); \( x_2 = 1, y_2 = 975 \)):
\( \Delta y = 975 - 985 = -10 \), \( \Delta x = 1 - 0 = 1 \).
Rate of change \( = \frac{-10}{1} = -10 \).
Since \( y \) decreases (negative rate), water decreases by 10 gallons per minute.

Answer:

The amount of water in tank B decreases by 10 gallons per minute. The rate of change for tank B is -10.