Direct Variation (proportion)

​Exploring Direct Variation

By Clifford Winter-Roach

cost vs gallons

“If gas costs $2.50 per gallon, how much will 4 gallons cost?

Multiple Choice

Which better describes this situation

• The cost depends on the number of gallons

• The number of gallons depends on the cost

cost = 2.5 * gallons

or

y = k * x ( x and y vary but k is constant )

direct variation:
a relationship of the form
y = k * x cost = 2.5 * gallons
k is the constant of variation or unit rate

Drag and Drop

Speed: driving at 60 mph, how far in 3 hours?

y = k * x



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180 miles

60 mph

3 hrs

Drag and Drop

Recipe scaling: 3 cups flour yields 24 cookies. How many cookies from 5 cups?



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40 cookies

8

5 cups

3 cups

Drag and Drop

Water filling: a tank fills at 15 liters per minute.





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liters

15

minutes

Drag and Drop

Currency conversion: 1 USD = 0.85 EUR.



y = k * x





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1 USD

0.85

EUR.

​Direct Variation

Direct variation is a situation with 2 variables.
One variable 'y' depends on the other variable 'x'
Formula: y = k * x (k is the 'rate' ....mph, gallons per minute )

Fill in the Blanks

Taxi fare: $3 per mile, find fare for 8 miles.

( include the $ sign )

Fill in the Blanks

Photocopying: $0.10 per page, cost for 45 pages.

( include the $ sign )

Fill in the Blanks

Recipe: 2 Tbsp sugar makes one serving;

how many servings from 12 Tbsp.

Fill in the Blanks

Speed: driving at 60 mph, how many minutes to travel 40 miles?

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__?__minutes