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. find the rate of change for the function that represents tank a. the amount of water in tank a? by? gallons per minute. the rate of change for tank a is? tank a: y = 900 - 11x tank b: | minutes, x | water in tank (gal), y | | 0 | 985 | | 1 | 975 | | 2 | 965 | | 3 | 955 |

Explanation:

Step1: Recall slope-intercept form

The slope - intercept form of a linear equation is \(y = mx + b\), where \(m\) is the slope (rate of change) and \(b\) is the y - intercept.

Step2: Identify \(m\) in Tank A's equation

For Tank A, the equation is \(y=900 - 11x\), which can be rewritten as \(y=- 11x + 900\). Comparing this with \(y = mx + b\), we see that \(m=-11\). The negative sign indicates that the amount of water is decreasing, and the rate of change (the rate at which water is leaking out) is 11 gallons per minute.

Answer:

The rate of change for the function representing Tank A is \(- 11\) (or we can say the amount of water in Tank A decreases by 11 gallons per minute, and the rate of change is \(-11\) gallons per minute).