1. Direct Variation

2. Direct Variation What you’ll learn …
To write and interpret direct variation equations
Model and solve problems using direct variation.

3. This is a graph of direct variation
This is a graph of direct variation.  If the value of x is increased, then y increases as well. Both variables change in the same manner.  If x decreases, so does the value of y.  We say that y varies directly as the value of x. 

4. Definition:
Y varies directly as x means that y = kx
where k is the constant of variation.
Another way of writing this is k =

5. Example 1a Identifying 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. x y 1 4 2 7 5 16 x y 2 8 3 12 5 20
k = _______
k = _______
Equation _________________
Equation _________________

6. Example 1b Identifying 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. x y -1 -2 3 4 6 7 x y -6 -2 3 1 12 4
k = _______
k = _______
Equation _________________
Equation _________________

7. Example 4a Using a Proportion
Suppose y varies directly with x, and x = 27 when y = Find x when y = -17.

8. Example 4b Using a Proportion
Suppose y varies directly with x, and x = 3 when y = 4. Find y when x = 6.

9. Example 4c Using a Proportion
Suppose y varies directly with x, and x = -3 when y = 10. Find x when y = 2.