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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

Sagot :

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 [tex]y=-26x+5274[/tex] and there will be [tex]1374[/tex] gallons of water in the pool after [tex]2[/tex] and a half hours.

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

Take points [tex](12, 4962)[/tex] and [tex](20, 4754)[/tex].

Here, [tex]x_1=12, y_1=4962, x_2=20, y_2=4754[/tex].

The equation is :

[tex](y-4962)=\frac{4754-4962}{20-12}(x-12)[/tex]

[tex](y-4962)=\frac{-208}{8}(x-12)[/tex]

[tex]8(y-4962)=-208(x-12)[/tex]

[tex]8y-39696=-208x+2496[/tex]

[tex]208x+8y-39696-2496=0[/tex]

[tex]208x+8y-42192=0[/tex]

[tex]8y=-208x+42192[/tex]

[tex]y=-\frac{208}{8}x+\frac{42192}{8}[/tex]

[tex]y=-26x+5274.[/tex]

The slope intercept form is [tex]y=mx+c[/tex], where [tex]m[/tex] is the slope and [tex]c[/tex] is the [tex]y[/tex]-intercept.

After [tex]2[/tex] and a half hours or [tex]150[/tex] minutes.

Put [tex]x=150[/tex] in the equation [tex]y=-26x+5274.[/tex]

[tex]y=-26\times 150+5274[/tex]

[tex]y=-3900+5274[/tex]

[tex]y=1374[/tex]

So, there will be [tex]1374[/tex] gallons of water in the pool after [tex]2[/tex] and a half hours.

Learn more about slope-intercept form here:

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

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