A large bucket that is a full of water has a small leak on the bottom. The bucket loses water at the rate of 0.5 gallons per min. After 6 mins the bucket contains exactly 9 gallons of water.
How many gallons of water were initially in the bucket? Also write an equation in point slope form to model the number of gallons (y) of water in the bucket after x minutes

Question

A large bucket that is a full of water has a small leak on the bottom. The bucket loses water at the rate of 0.5 gallons per min. After 6 mins the bucket contains exactly 9 gallons of water.  
How many gallons of water were initially in the bucket?  Also write an equation in point slope form to model the number of gallons (y) of water in the bucket after x minutes

phagey · Answer

@Michele_Laino

michele_laino · Answer

hint:
if I call with $y_0$ the initial amount of water of the bucket, and with $x$ the number of minutes, then, after $x$ minutes the amount of water, is:
$y_0-0.5 \cdot x$

michele_laino · Answer

now, if we specialize at the case $x=6$, then we can write:
$$\huge  {y_0} - 0.5 \cdot 6 = 9$$
please solve for $y_0$

phagey · Answer

i got 12 @Michele_Laino

phagey · Answer

@Michele_Laino

michele_laino · Answer

ok! So, the initial amount of water is $12$ gallons
Now, after $x$ minutes, the remaining amount of water, will be:
$12-0.5 \cdot x$, since we have to start from the initial amount which is $12$ gallons

michele_laino · Answer

so, what is the equation in the point slope form ?

phagey · Answer

i really dont know @Michele_Laino

michele_laino · Answer

it is simple, the generic amount of water contained by the bucket after $x$ minutes, is the dependent variable $y$, so the requested equation, is:
$y=12-0.5x$

phagey · Answer

ohhh i feel so stupid thank you @Michele_Laino

michele_laino · Answer

thanks!! :)