Algebra 2 Notes
2-2 Direct Variation
Date:
Direct Variation: A Function whose formula can be written as _________________ or ____________,
where 𝑘 ≠ 0. X represents the ____________ values, and y represents ____________ values.
Constant of Variation: The formula ______________ says that, except for (0,0), the ratio of all outputinput pairs equals the constant k. This constant k is the constant of variation.
Example 1: Identifying Direct Variation from Tables.
For each function, determine whether y varies directly with x. If so, what is the constant of variation and
the function rule?
A)
B)
X
Y
X
Y
1
2
1
4
3
6
2
8
4
8
3
11
Example 2: Identifying Direct Variation From Equations
For each function, determine whether y varies directly with x. If so, what is the constant of variation?
A) 3𝑦 = 7𝑥
B) 7𝑦 = 14𝑥 + 7
Barr
Example 3: Using a Proportion to Solve a Direct Variation
Suppose y varies directly with x, and y = 9 when x = -15. What is y when x = 21?
Example 4: Using Direct Variation to Solve a Problem
A salesperson’s commission varies directly with sales. For $1000 in sales, the commission is $85. What is
the commission for $3200 in sales?
Example 5: Graphing Direct Variation Equations
What is the graph of each direct variation equation?
3
A) 𝑦 = 4 𝑥
B) 𝑦 = −2𝑥
Barr