Final answer:
The function describes how the volume of water decreases as time passes, with a slope of -100 indicating the tank is emptied at a rate of 100 gallons per minute. At zero minutes, there are 20,000 gallons in the tank, represented by the y-intercept on the graph.
Step-by-step explanation:
The function given is f(m) = 20,000 - 100m, where m is the number of minutes that have passed since the pump started emptying the full tank. When graphing the equation on a coordinate plane, m is on the horizontal axis (independent variable), and f(m) or the volume of water in gallons is on the vertical axis (dependent variable).
The slope of this equation is -100, which means it's negative. A negative slope indicates that the line moves down the y-axis as the x-value (minutes, in this case) increases, showing a decrease in the water level as time passes. The slope describes the rate at which the tank is being emptied, with 100 gallons of water being pumped out per minute.
At zero minutes, f(0) = 20,000 gallons, representing the initial volume of water in the tank. This value is the y-intercept of the graph and is the point where the line crosses the y-axis.