Question

the table below represents the amount of water, in gallons, draining from a tank over time. write the equation of the linear function shown on the graph in slope intercept form. ( y = mx + b ) ( y=-50x + 800 ) explain what the slope means in the context of this problem.

Explanation:

In the linear equation \(y = mx + b\), the slope \(m\) represents the rate of change. Here, \(x\) is time (in minutes) and \(y\) is the amount of water (in gallons). The slope \(m=- 50\) means that for each additional minute (\(\Delta x = 1\)), the amount of water in the tank decreases by 50 gallons (\(\Delta y=-50\)). So, it represents the rate at which water is draining from the tank.

Answer:

The slope \(-50\) means that the amount of water in the tank is decreasing at a rate of 50 gallons per minute.