A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 55 ​seconds, the gauge on the bottle indicates that it contains 1919 ounces of water. After it has been filling for 1111 ​seconds, the gauge indicates the bottle contains 3737 ounces of water. Let y be the amount of water in the bottle x seconds after the faucet was turned on. Write a linear equation that relates the amount of water in the​ bottle, y, to the time x.

Answer:[tex]y=3x+4[/tex]Step-by-step explanation:Let y be the amount of water in the bottle x seconds after the faucet was turned on.We have been given that the gauge on the bottle indicates that it contains 19 ounces of water after it has been filling for 5 seconds. After it has been filling for 11 ​seconds, the gauge indicates the bottle contains 37 ounces of water. We have two points on the line [tex](5,19)[/tex] and [tex](11,37)[/tex].Let us find slope of the line passing through these points.[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex][tex]m=\frac{37-19}{11-5}[/tex][tex]m=\frac{18}{6}[/tex][tex]m=3[/tex]We will write our required equation in slope-intercept form [tex]y=mx+b[/tex], where, m represents slope and b represents the y-intercept.Let us find y-intercept by substituting [tex]m=3[/tex] and coordinates of point [tex](5,19)[/tex] in slope intercept form.[tex]19=3\cdot 5+b[/tex][tex]19=15+b[/tex][tex]19-15=15-15+b[/tex][tex]4=b[/tex]Therefore, our required equation would be [tex]y=3x+4[/tex].