Name: ________________________________________
Bl:___
Direct and Inverse Variation
So, you’re telling me that k is basically m…
Direct Variation:
• Formal Definition: Direct variation is a relationship between variables such that each
variable is directly proportional to the other
• What it Means: In direct variation, you always multiply x times the same number to find
y. (Example y = 2x)
• THE GRAPH OF DIRECT VARIATION ALWAYS GOES THROUGH THE
_______________.
K – the constant of variation
• Equation for Direct Variation
– _________________________
• x and y are always the variables
• k = the constant of variation (the number you multiply by x to find y)
•
_______________________
Direct Variation with Table
x
1
2
3
4
y
6
9
12


3
k = ______________
Equation: _____________________
Direct Variation Statement:
• Assume y varies directly as x. If x = 5 when y = -15, write an equation for y.
– Find k: _______________________
– Write the equation: ________________________
– Plug in what you know and find what you don’t: _________________________
Finding y:
• Assume y varies directly as x, if x = 10 when y = 3, what is y when x = 15
– Find k: _______________________
– Write the equation: ________________________
– Plug in what you know and find what you don’t: _________________________
Finding x:
• Assume y varies directly as x, if x = -2 when y = 6, find x when y = -3.
– Find k: _______________________
– Write the equation: ________________________
– Plug in what you know and find what you don’t: _________________________
Name: ________________________________________
Bl:___
Inverse Variation:
• Formal Definition: the values of two variables change in such a way that as one variable
increases, the other decreases
•
What it Means: In inverse variation the product of y and x is always equal
K – the constant of variation
• Equation for Inverse Variation
– ____________________
•
y and x remain variables k = constant of variation
– ________________________
Inverse Variation Table:
x
4
16
32
64
y
2
1
½


8
k = ______________
Equation: _____________________
Writing the Equation:
• Assume y varies inversely as the value of x. If y = 3 when x = 7, write an equation for y.
– Find k: ______________________
– Plug in to the equation: __________________________
Finding y
• Assume y varies inversely as x. If y = 4 when x = 3, find y when x = 6.
– Find k: _______________________
– Write the equation: ________________________
– Plug in what you know and find what you don’t: _________________________
Finding x
• Assume y varies inversely as x, if y = 3 when x = 10, find x when y = 15.
– Find k: _______________________
– Write the equation: ________________________
– Plug in what you know and find what you don’t: _________________________