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 k using, 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

Graphs of Direct Variations

Writing a Direct Variation from a Table

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

Examples of Graphs of Inverse Variations

Graphing an Inverse Variation

• Pg 688 Problem 3

Comparing Direct & Inverse Variations

Determining Direct or Inverse Variation

Identifying Direct or Inverse Variation

• Page 689 Problem 5