A plugged sink is filled with water. After the plug is removed, water drains at a constant rate. The amount of water remaining in a sink is given by the equation \(A=15-5x\), where \(x\) is the number of minutes after the plug is removed and \(A\) is the volume, in gallons, of water remaining in the sink. In the equation, what are the meanings of the numbers \(15\) and \(5\)?

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Many linear models are written in the form \(y=mx+b\).

$$ y=mx+b$$ $$ A=-5x+15 $$

Typically, the \(y\)-intercept refers to the initial quantity and the slope \(m\) will refer to a rate.

We can eliminate the first two answer choices, since the number \(5\) corresponds to the slope, or rate, in the equation.

Among the remaining choices, the difference lies in whether the number \(5\) refers to an increase or decrease in the volume of the sink. Based on the question, we can interpret that the water level in the sink will decrease over time as water is drained when the plug is removed.