AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
May 09, 2016
AFDA - Direct, Inverse and Joint Variation Models
Variation is a special way that x and y
can be related to one another; the
three types of variation you need to
know are.....
Direct
Joint
"y varies directly with x"
Inverse
"z varies jointly with x and y"
For each model, k is the constant of variation.
"y varies inversely with x"
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
May 09, 2016
Variation
Variation is a special way that x and y can be related to one another
The 3 types of variation you need to know are:
Direct
"y varies directly with x"
k is the constant of variation
Inverse
"y varies inversely with x"
k is the constant of variation
Joint
"z varies jointly with x and y"
k is the constant of variation
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
DIRECT VARIATION
May 09, 2016
y = kx
1. The variables x and y vary directly when x = 6 and y = 18.
a) Find the value of k
b) Write an equation relating x and y
c) Use the equation you wrote to find x when y = -6
2. The variables x and y vary directly when x = 20 and y = 5.
a) Find the value of k
b) Write an equation relating x and y
c) Use the equation you wrote to find y when x = 12
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
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Additional Practice:
3. Suppose y varies directly as x, and y = 20 when x = 4. Find y when x = 9.
When we see the phrase “y varies directly as x” that tells us when should be using
the equation: ___________________________
The next piece of information tells use that y = 20 and x = 4. We will use this
information to find the value of k: _________________________
Now use the fact that k = 5 to find the value of y that the problem is asking
for.
You should be careful to note that it is possible for other variables to be used in
a problem. Based on the wording in the problem, this will tell you how to set up
your initial equation.
4. Suppose a varies directly as x, and a = 15 when x = 2. Find a when x = 8.
Note that there are different variables, but the initial equation used to find k will
be similar to what was used before. Once we find k, then we use our equation
again to find a.
Now use that value to find a.
http://www.algebralab.org/lessons/lesson.aspx?file=Algebra_LinearEqDirectVariation.xml
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
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http://www.algebralab.org/practice/practice.aspx?file=Algebra_DirectVariation.xml
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AFDA_Direct_Inverse_Joint_Variation_Day1.notebook
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