Direct Variation

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

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. 

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

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 _________________

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 _________________

Example 4a Using a Proportion Suppose y varies directly with x, and x = 27 when y = -51. Find x when y = -17.

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

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