A faucet is used to add water to a large bottle that already contained some water. After it has been filling for 5 seconds, the gauge on the bottle indicates that it contains 22 ounces of water. After it has been filling for 13 seconds, the gauge indicates the bottle contains 54 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 models the amount of water in the bottle in terms of x.

Question

anonymous · Answer

1. lets say there was $V(t=0)=V_0$ amount of water in the faucet initially
2. after t = "5", $V(t=5)=22$
3. after t="13", $V(t=13)=54$

by what amount does the volume change?
hint-> linearly
so assume a straight line
$V(t)=mt+b$
follow?

anonymous · Answer

or equation of a straight line passing through two points

anonymous · Answer

y = 4x + 4

anonymous · Answer

$$\frac{x-x_1}{x_1-x_2}=\frac{y-y_1}{y_1-y_2}$$

anonymous · Answer

$$4(x-5)=y-22$$
you can check py substituting x="5" and x="13"