Section 4.7 - Straight to the Point: Direct Variation

Section 4.7 - Straight to the Point: Direct Variation

Goal: To be able to model, and use, the equation given direct variation.

After 0 hours, how many gallons of water are in the pool?

​

After 3 hours, how many gallons of water are in the pool?​

​Volume = rate * time

The pool holds 21,000 gallons of water, that was emptied, is being filled by a garden hose at a constant rate of 300 gallons per hour.

​A swimming pool...

Exploring This

Is the relationship between the water in the pool and time a linear one? How do you know.

Fill in the Blank

So, let's do a little more with this. Remember - for our pool;

Volume = rate * time where the rate is 300 gallons per hour. After 5 hours, there are ____ gallons of water in the pool.

Fill in the Blank

One more time; volume = rate * time where the rate is 300 gallons per hour. After 20 hours, there are ____ gallons of water in the pool.

Multiple Choice

Which of the following would represent the correct equation that models this change in volume of pool water? Given V is volume and t is time.

• $$V=\frac{300}{t}$$  

• $$t=\frac{V}{300}$$  

• $$V=300t$$  

• $$t=300V$$  

​What do we notice?

As the time increases - the total volume of water in the pool increases. Since both quantities are increasing, this represents DIRECT VARIATION. ​

Multiple Choice

Why do we want to know that the pool gets filled following the equation V = 300t? Because now you can state that it takes ___ hours to fill the 21,000 gallon pool.

• 70

• 700

• 7

• None of These

Multiple Choice

Which of the given graphs is a direct variation?

• A
• B
• C
• D

Multiple Choice

Is this a direct variation?

• yes
• no

Multiple Choice

Is this a direct variation?

• yes
• no

Multiple Choice

Does y varies directly as x?

• Yes; k = 9

• No

Multiple Choice

Does y varies directly as x?

• Yes; k = 5

• No

Multiple Choice

In a direct variation, y=39 when x=3.  Find the value of y when x=2.

• 26
• 3
• 58.5
• 2

Multiple Choice

y varies directly with x. If y = 20 when x = 4, what is y when x = -2 ?

• -10

• 10

• -5

• 5