Algebra 2/Trig
Name: ______________________________
Date: __________ Block: ______
Section 9.1: Direct and Inverse Variation
Direct Variation:
 x and y show direct variation if

k is called the ____________________________________________________________.

Another phrase for “Direct Variation” is ______________________________________.

The graph of y = kx goes through the _____________________ .

An example formula is ______________________
- Distance and time vary directly, which means as time increases, distance increases OR as time decreases,
distance decreases.
The variables x and y vary directly. Write an equation that relates the two variables.
Then find y when x = 6.
1.) x = 2, y = 7
2.) x = 24, y = 6
3.) x = .8, y = -1.6
4.) If y varies directly with x, and y = 3 when x = 2, then what is the value of y when x = 6?
A) 1
B) 2
C) 3
D) 6
E) 9
5.) Suppose y is directly proportional to x2. If y = 16 when x = 2, what is the value of y when x is 7?
6.) If y is directly proportional to x2 and y = 18 when x = 3, which of the following could be the value of x
when y = 8?
A) -4
B) -2
C) 1
D) 4/3
E) 6
7.) If y varies directly with x, and y = 24 when x = 8, then what is the value of x when y = 33?
8.) If y varies directly with x, and y = 52 when x = 13, then what is the value of x when y = 14?
9.) If y varies directly with the table to the right, then when x = 5.5, what is the value of y?
x
1
2
3
4
y
3
6
9
12
Inverse Variation
 x and y show inverse variation if

Another phrase for “Inverse Variation” is ______________________________________.

An example formula is ________________
- Density and volume vary indirectly, which means as volume increases, density decreases.
The variables x and y vary inversely. Use the given values to write an equation relating x and y.
Then find y when x = 4.
10.) y = 6, x = 1.5
11.) y = 2, x = 8
12.) If y is inversely proportional to x, and y = 3 when x = 2, then what is the value of y when x = 6?
A) 1
B) 2
C) 3
D) 6
E) 9
13.) Suppose y varies indirectly to the square of x. When x is 2, y is equal to 25. What is the value of y when x
is 10?
A) 1
B) 4
C) 5
D) 10
E) 25
14.) If y varies indirectly with x 2 and y = 9 when x = 3, then what is the value of x when y = 18?
Direct variation, Inverse variation or Neither? To answer this, we need to ___________________________
y
15.) xy = 4.8
16.) x 
17.) y = 2x + 3
18.) x = 3y
1.5
Applications: Use direct and inverse variation to solve the following problems.
19) The amount of money earned on a job is directly proportional to the number of hours worked. If $36 is earned for
8 hours of work, how much is earned for 30 hours of work?
20) The cost per person to rent a mountain cabin is inversely proportional to the number of people who share the rent. If
the cost is $36 per person when 5 people share, what is the cost per person when 8 people share?