Direct, Inverse, and Joint Variation

Two quantities, one constant holding them together.

12 problems · about 21 minutes · A-CED.A.2, A-CED.A.4

NameDate

Figure — use these to answer the problems

Raise k and watch the whole hyperbola move away from the axes without ever touching them.

y = 2/x + 0

k, the constant2

Figure 1

Straightforward practice. Get the method working first.

5 problems

y varies inversely with x, and y = 10 when x = 3. What is k?
Answer
2
Which graph belongs to direct variation?
- A line through the origin.
- A hyperbola near the axes.
y varies directly with x, and y = 20 when x = 4. What is k?
Answer
Same relationship. What is y when x = 7?
Answer
y varies inversely with x, and y = 6 when x = 4. What is k?
Answer

The same ideas with more to keep track of.

3 problems

Same relationship. What is y when x = 8?
Answer
y varies jointly with x and z, with k = 2. What is y when x = 3 and z = 5?
Answer
Pressure varies inversely with volume, and k = 100. What is the pressure when the volume is 25?
Answer

Mixed problems. Work out what kind of question it is before you start.

4 problems

Sort each pairing by the kind of variation it shows.
Write each item under the heading it belongs to: x = 2, y = 6 and x = 4, y = 12 · x = 2, y = 12 and x = 4, y = 6 · Hours worked and total pay · Speed and travel time over a fixed distance
Direct
Inverse
y varies directly with x. When x = 9, y = 27. What is x when y = 12?
Answer
The Wages
Pay varies directly with hours. 6 hours pays $90. What does 10 hours pay, in dollars?
Answerdollars
The Workers
Time varies inversely with the number of workers. 4 workers take 12 days. How many days do 6 workers take?
Answerdays