Question

max puts a stopper in the bathtub and turns on the faucet at t = 0. after 5 minutes, there are 11 gallons of water in the tub and after 10 minutes, there are 22 gallons in the tub. write an equation that relates the number of gallons, g, to the time, t. does the relationship represent a linear function? justify your response. options: g = 2.2t; the equation represents a linear function because the equation is in the form y = mx. g = 2.2t; the equation does not represent a linear function because the equation is not in the form y = mx + b. g = 4.4t; the equation represents a linear function because the equation is in the form y = mx. g = 4.4t; the equation does not represent a linear function because the equation is not in the form y = mx + b.

Explanation:

Step1: Find the rate of water flow

The rate $m$ is $\frac{\text{Change in gallons}}{\text{Change in time}} = \frac{22-11}{10-5} = \frac{11}{5} = 2.2$ gallons per minute.

Step2: Determine the linear equation

At $t=0$, the tub has 0 gallons, so the y-intercept $b=0$. The equation is $g = mt + b = 2.2t + 0 = 2.2t$.

Step3: Verify linear function form

A linear function can be written as $y=mx$ (a special case of $y=mx+b$ where $b=0$), so $g=2.2t$ is linear.

Answer:

A. $g = 2.2t$; The equation represents a linear function because the equation is in the form $y = mx$.