Question

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 17 ounces of water. after it has been filling for 11 seconds, the gauge indicates the bottle contains 35 ounces of water. let w be the amount of water in the bottle t seconds after the faucet was turned on. write a linear equation that models the amount of water in the bottle in terms of t. select a single answer $w = -3t + 32$ $w = 3t + 24$ $w = 3t + 2$ $w = \frac{1}{3}t + \frac{46}{3}$

Explanation:

Step1: Define linear form

A linear equation has the form $w = mt + b$, where $m$ is the rate (slope) and $b$ is the initial water amount.

Step2: Calculate slope $m$

Use two points $(t_1,w_1)=(5,17)$ and $(t_2,w_2)=(11,35)$.
$m = \frac{w_2 - w_1}{t_2 - t_1} = \frac{35 - 17}{11 - 5} = \frac{18}{6} = 3$

Step3: Solve for initial $b$

Substitute $m=3$, $t=5$, $w=17$ into $w=mt+b$.
$17 = 3(5) + b$
$17 = 15 + b$
$b = 17 - 15 = 2$

Step4: Write final equation

Substitute $m=3$ and $b=2$ into $w=mt+b$.
$w = 3t + 2$

Answer:

$w = 3t + 2$