I need help please

Question

 A swimming pool is being drained at a constant rate of 3 inches (depth of the water) per hour. The depth of the water after 5 hours is 32 inches. Write the equation for this function in point slope form. (7 points) pool drains at 3 inches per hour, after 5 hours 32 inches= depth of the pool water d(h)=f-3h where f= depth when full, h= hours, d= depth after h hours 32=f-3(5), f=32+15=47 inches when full d=47-3h pool will be empty when d=0=47-3h. Then graph your function to find how long it will take to empty the pool completely. 

Answer 1

Hi James,

Let:

x=time

y=depth

You were given a constant rate of three inches per hour, but this is a decrease. This is a rate, which makes it a slope, so:

m= -3

Now, point-slope form is:

y-y₁=m(x-x₁) where:

y₁=y-coordinate

x₁=x-coordinate

You were given that the depth at 5 hours is 32 inches, so that equates to the point (5,32) and means:

x₁=5

y₁=32

m= -3

Your final equation is:

y - 32 = -3(x-5)

Now, you were asked to graph this and determine when the pool empties completely.

To do the graph, just substitute values. First, plug 0 in for x. This gives:

y-32=-3(0-5)

y-32=15

y= -17

First point on graph (0, -17)

Try -1 and 1 for x and you will have 3 points, which should be enough for a graph.

Now, you want the time it takes to empty the pool completely. That means you want the depth, y, to be 0. So set y₁=0 in your equation.

y-32= -3(x-5)

0-32= -3(x-5)

-32= -3x + 15

-47=-3x

x=47/3

About 15 hours, 40 minutes.

I hope this helps.

Answer 2

Hi James, is there a way you can take a screenshot of the problem? That would help with understanding the question more.