the equation that models this direct variation.
[tex]m=\frac{4}{3} g[/tex]
[tex]\frac{28}{3} \; or \; 9\frac{1}{3}[/tex] 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 [tex]y=mx[/tex]
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
[tex]m=k(g)[/tex]
Now we find out k
a broken faucet leaks one gallon of water every 1 1/3 months
[tex]m=1\frac{1}{3}=\frac{4}{3} \\gallons g=1\\m=kg\\\frac{4}{3} =k(1)\\k=\frac{4}{3}[/tex]
Now we replace the value of 'k'
The equation that models direct variation is
[tex]m=\frac{4}{3} g[/tex]
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
[tex]m=\frac{4}{3} g\\m=\frac{4}{3} (7)\\\\m=\frac{28}{3}\\[/tex]
Learn more : brainly.com/question/472621
