1. Section 3 Direct Variation
Chapter 2
Section 3
Direct Variation

3. Writing and Interpreting a Direct Variation
Direct Variation – a linear function defined by an equation of the form y = kx, where k ≠ 0
Constant of Variation, k, the ratio of y : x (usually written as a fraction )

4. Identifying a Direct Variation from a Table
For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. b) a) x y 1 4 2 7 5 16 x y 2 8 3 12 5 20
Since the ratios are not equal this is not a direct variation.
y does not vary directly with x.
Since the fractions are equal, the constant of variation (k) is 4. The equation is y = 4x.

5. Identifying Direct Variation from an equation
For each function determine whether y varies directly with x. If so, find the constant of variation.
a) 3y = 2x
y = 2x Does this fit the form of y = kx?
y = 2/3 x Solve for y.
Does this fit the form of y = kx?
y does not vary directly with x
What is k?

6. Using Proportions
You can use proportions to solve some equations that do not require the constant of variation.
Solve: Suppose y varies directly with x and x = 27 when y = Find x when y = -17.

7. Homework
P. 74 #