the equation that models this direct variation.
\(m=\frac{4}{3} g\)
\(\frac{28}{3} \; or \; 9\frac{1}{3}\) months will it take for the faucet to leak 7 gallons of water
Given :
the amount of months that pass, m , varies directly with the amount of gallons that are leaked, g.
When y varies directly with x then equation is \(y=mx\)
Now we use the given information to frame equation
Month varies directly with the amount of gallons leaked
The equation that models direct variation is
\(m=k(g)\)
Now we find out k
a broken faucet leaks one gallon of water every 1 1/3 months
\(m=1\frac{1}{3}=\frac{4}{3} \\gallons g=1\\m=kg\\\frac{4}{3} =k(1)\\k=\frac{4}{3}\)
Now we replace the value of 'k'
The equation that models direct variation is
\(m=\frac{4}{3} g\)
Now we find out how many months will take for the faucet to leak 7 gallons of water
Substitute 7 for g in the above equation
\(m=\frac{4}{3} g\\m=\frac{4}{3} (7)\\\\m=\frac{28}{3}\\\)
Learn more : brainly.com/question/472621
