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A farmer has two water tanks that drain at a rate of 2.5 gallons per minute. He is considering replacing the existing tanks with new ones, either Model S or Model T. Information about the new tanks is shown below. All tanks, old and new, hold 100 gallons of water and drain at a constant rate.


Select all options that correctly represent the situation.


The equation, y = 4x + 86, represents the Model T tank.


The existing tanks drain the slowest at 2.5 gallons per minute.


The equation, y = -3x + 100, represents the Model S tank.


The equation, y = 2.5x + 100, represents the existing tanks.


The Model S tank drains the fastest at 3 gallons per minute.


The Model T tank drains the fastest at 3.5 gallons per minute.

Answer 1

Answer:

(c) The equation, y = -3x + 100, represents the Model S tank.

(f) The Model T tank drains the fastest at 3.5 gallons per minute.

Step-by-step explanation:

Given

See attachment for models S and T

First, we calculate the equation of both models

Model S

$(x_1,y_1) = (0,100)\\\\(x_2,y_2) = (6,82)$

Calculate drainage rate (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{82-100}{6-0}$

$m = \frac{-18}{6}$

$m = -3$ -- This implies that model S drains at 3 gallons per minutes

The equation is:

$y = m(x - x_1) + y_1$

$y = -3(x - 0)+100$

$y = -3(x)+100$

$y = -3x+100$

Model T

$(x_1,y_1) = (0,100)\\\\(x_2,y_2) = (4,86)$

Calculate drainage rate (m)

$m = \frac{y_2 - y_1}{x_2 -x_1}$

$m = \frac{86-100}{4-0}$

$m = \frac{-14}{4}$

$m = -3.5$ -- This implies that model T drains at 3.5 gallons per minutes

The equation is:

$y = m(x - x_1) + y_1$

$y = -3.5(x - 0)+100$

$y = -3.5(x)+100$

$y = -3.5x+100$

From the calculations above, the following options are true:

(c) and (f)

Answer 2

It is required to find which statements are true.

The statements that are true are

The equation, y = -3x + 100, represents the Model S tank.

The Model T tank drains the fastest at 3.5 gallons per minute.

Equation of a line is

$y=mx+c$

where,

$y=\text{Gallons of water left}$

$x=\text{Minutes passed}$

$m=\text{Slope}=\dfrac{\Delta y}{\Delta x}$

$c=\text{Y intercept}$

The equation of the line for model S is

$y-100=\dfrac{82-100}{6-0}(x-0)\\\Rightarrow y-100=-3x\\\Rightarrow y=-3x+100$

The option C is true.

The equation of the line for model T is

$y-100=\dfrac{86-100}{4-0}(x-0)\\\Rightarrow y-100=-3.5x\\\Rightarrow y=-3.5x+100$

The slope or rate of drain is 3.5 gallons per minute.

So, option F is true.

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