Direct and Inverse Variation
Direct Variation
Inverse Variation
An equation of the form ________________,
where ______________.
An equation of the form ______________,
where ___________________.
Example: y = 2x
Example: y 
Is it linear? How do you know?
Is it linear? How do you know?
Graph the example:
Graph the example:
Stephanie Moore 2012
2
x
Direct Variation
Inverse Variation
1. An equation of the form ______________________,
where _____________________________.
1. An equation of the form ___________________,
where _______________________.
2. As x ______________, y _________________.
2. As x __________________, y ______________.
3. A direct variation equation ______________ passes
through the ___________________.
3. An inverse variation equation does not pass through
the __________________.
4. When graphed, a direct variation equation will be a
__________________ and __________ will represent
the _______________ of the _____________.
4. When graphed, an inverse variation equation will be a
________________ and _________ will not represent
the _____________ (because it is not a ________.)
5. The constant of proportionality in a direct variation is
represented by the _____________ of the
_______________ variable (____) to the
_______________ variable (____).
5. The constant of proportionality in an inverse variation
is represented by the _____________ of the
_______________ variable (____) and the
_______________ variable (____).
6. Examples:
6. Examples:
Stephanie Moore 2012
Direct and Inverse Variation KEY
Direct Variation
Inverse Variation
k
____,
x
An equation of the form ___y = kx______,
An equation of the form ____ y 
where __k does not equal 0_______.
where _ k does not equal 0__.
Example: y = 2x
Example: y 
Is it linear? How do you know?
Is it linear? How do you know?
Yes, because it can be written in standard
form
No, because it cannot be written in standard
form
Graph the example:
Graph the example:
Stephanie Moore 2012
2
x
Direct Variation
1. An equation of the form _____y=kx________, where
__k does not equal 0____.
Inverse Variation
k
1. An equation of the form ____ y  _____, where
x
_where k does not equal 0____.
2. As x __increases_____, y ___ increases ___.
2. As x __ increases ___, y __decreases___.
3. A direct variation equation __always___ passes
through the __the origin______.
3. An inverse variation equation does not pass through
the ___origin_____.
4. When graphed, a direct variation equation will be a
___line_____ and ___k____ will represent the
__slope_____ of the ___line____.
4. When graphed, an inverse variation equation will be a
__parabola____ and ___k__ will not represent the
___slope___ (because it is not a __line__.)
5. The constant of proportionality in a direct variation is
represented by the __ratio___ of the __dependent__
variable (_y_) to the ___independent___ variable
y
 k or y = kx
(__x__).
x
5. The constant of proportionality in an inverse variation
is represented by the __product__ of the
__dependent____ variable (_y_) and the
_independent___ variable (_x_).
k
K = yx or y 
x
6. Examples:
a) hours worked and pay
6. Examples:
a) time it takes for ice to melt varies inversely with the
Stephanie Moore 2012
b) distance and time
c) iTunes (amount of songs purchased and total amount
spent)
d) length of sides of a figure and perimeter of the figure
Stephanie Moore 2012
temperature
b) Number of people eating pizza and number of pieces
of pizza available per person
c) length and width of a rectangle if the area remains
constant