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A pool is being drained at a constant rate. The amount of water is a function of the number of minutes the pool has been draining, as shown in the table. Write an equation in slope-intercept form that represents the function. Then find the water in the pool after two and a half hours. 
Time (mi)       12--------20------50
Volumne (gal) 4962--4754--3974

Verified Answer :

davy94

Answer:

Using the first two values in the table, we can first find the slope to write an equation of a line, so we have


[4754 - 4962 ] / [20 - 12 ] = -26


So we have


y - 4754 = -26(x - 20)  


y - 4754  = -26x + 520


y = -26x + 5274


Let's confirm that the amount after 50 minutes is correct


y = -26(50) + 5274  = 3974


So after  2 + 1/2 hrs  (150 min) we have


y = -26(150) + 5274  = 1374 gallons

Step-by-step explanation:

The equation in the slope-intercept form is \(y=-26x+5274\) and there will be \(1374\) gallons of water in the pool after \(2\) and a half hours.

The equation of a line that passes through two points \((x_1, y_1)\) and \((x_2, y_2)\) is \((y-y_1)=\frac{y_2-y_1}{x_2-x_1}(x-x_1)\).

Take points \((12, 4962)\) and \((20, 4754)\).

Here, \(x_1=12, y_1=4962, x_2=20, y_2=4754\).

The equation is :

\((y-4962)=\frac{4754-4962}{20-12}(x-12)\)

\((y-4962)=\frac{-208}{8}(x-12)\)

\(8(y-4962)=-208(x-12)\)

\(8y-39696=-208x+2496\)

\(208x+8y-39696-2496=0\)

\(208x+8y-42192=0\)

\(8y=-208x+42192\)

\(y=-\frac{208}{8}x+\frac{42192}{8}\)

\(y=-26x+5274.\)

The slope intercept form is \(y=mx+c\), where \(m\) is the slope and \(c\) is the \(y\)-intercept.

After \(2\) and a half hours or \(150\) minutes.

Put \(x=150\) in the equation \(y=-26x+5274.\)

\(y=-26\times 150+5274\)

\(y=-3900+5274\)

\(y=1374\)

So, there will be \(1374\) gallons of water in the pool after \(2\) and a half hours.

Learn more about slope-intercept form here:

https://brainly.com/question/21366542?referrer=searchResults

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