Direct Variation Section 1 9 Notes Direct Variation

Direct Variation Section 1. 9

Notes: Direct Variation When two variable quantities have a constant ratio, their relationship is called a ________. The constant ratio is called the ___________. The constant of variation is also known as the ___________.

What is a Direct Variation? A special equation in the form: y = kx k is called the “constant of variation”; it is also the slope of the equation The variables have a direct relationship; as one increases/decreases, so does the other The graph of a direct variation always passes through the origin Example: y = 3 x

Determining a Direct Variation FROM EQUATIONS: Put equation into form (y = ) and determine if it fits the pattern y = kx Are these direct variations? y=x y = 2 x – 1 3 x = 5 y

Notes: Determine a Direct Variation Not all situations with a constant rate of change are proportional relationships. Likewise, not all linear functions are direct variations.

Determining a Direct Variation FROM TABLES: Solve each ordered pair for k (k = y/x) If k is constant for each ordered pair, you have a direct variation

Examples X Y -6 9 -2 1 1 -1. 5 3 6 8 -12 8 -4

Graphing Direct Variations Always know 1 point on the line: (0, 0) Use k (the slope) to get additional points

Examples: Determine whether each linear relationsh is a direct variation. If so, state the constant of proportionality 1. Pictures, x 3 4 5 Profit, y 24 32 40

Year, x 5 10 15 Height, y 12. 5 25 37. 5

Essential Question How can you determine if a linear relationship is a direct variation from an equation? A table? A graph? _____________________ _____________________ __