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 Blanks

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 Blanks

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