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Direct Variation & Inverse Variation (SOL A.8). Chapters 5-2 & 11-6. Direct Variation. If the ratio between two variables is a constant, than a direct variation exists. A direct variation can be written in the form of y = kx , where k is the constant of variation. . Inverse Variation.
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Direct Variation & Inverse Variation (SOL A.8) Chapters 5-2 & 11-6
Direct Variation • If the ratio between two variables is a constant, than a direct variation exists. • A direct variation can be written in the form of y = kx, where k is the constant of variation.
Inverse Variation • Is the product of two variables is a constant, then an inverse variation exists. • An inverse variation can be written in the form y = k/x or xy = k.
Examples of Direct Variations • 7y = 2x • 3y + 4x = 8
Your Turn • Does the following represent a direct variation? If so, find the constant of variation. • 4x + 5y = 0
Writing an equation for a direct variation • First thing----find the constant of variation kusing, an ordered pair, other than (0, 0), that you know is a solution of the equation. • Look at Problem 2 on page 300 in your textbook.
Graphing a Direct Variation • Problem 3 on page 300
Moving on to Inverse Variation • An equation of the form xy = k or y = k/x, where k ≠ 0, is an inverse variation. • The constant of variataion for an inverse variation is k, the product x ∙ y for an ordered pair (x, y) that satisfies the inverse variation.
Writing an Equation Given a Point • Problem 1 on page 686
Using Inverse Variation • Problem 2 page 687
Graphing an Inverse Variation • Pg 688 Problem 3
Identifying Direct or Inverse Variation • Page 689 Problem 5