Atub of water is emptied at a rate of 3 gallons per minute. the equation y –12 = –3(x – 1) models the amount of water remaining, where x is time (in minutes) and y is the amount of water left (in gallons). analyze the work shown below to determine the initial amount of water.

I don't see any work to analyze, but if you want to find the initial amount of water you can do that by rewriting the given equation in slope-intercept form.  In this form the y-intercept will represent the initial amount of water.

y - 12 = -3(x - 1)
y = -3x + 3 + 12
y = -3x + 15   So the initial amount of water was 15 gallons.