NOTES 2.3 & 9.1 Direct and Inverse Variation. Direct Variation A function in the form y = kx, where k is not 0 Constant of variation (k) is the coefficient.

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NOTES 2.3 & 9.1 Direct and Inverse Variation

Direct Variation A function in the form y = kx, where k is not 0 Constant of variation (k) is the coefficient of x. x and y are said to vary directly with each other.

Is an equation a direct variation? Solve for y. Does it fit the form y = kx? Examples: 1. 2y = 5x x = 6y

Writing an Equation Given x and y 1. Use k = to find the constant of variation 2. Write the new direct variation function. Examples 3. (5, 1) 4. x = -5, and y = -10

Using a Proportion Find the missing value for the direct variation. 5. If y = 4 when x = 3, find y when x = If y = 10 when x = -3, find x when y = 2.

Direct Variations and Tables xy xy Tell whether y varies directly with x. If it does, write an equation for the direct variation.

Inverse Variation An equation in the form xy = k or y =, where k is not 0 Constant of variation (k) is the product of x and y for an ordered pair (x, y) Suppose y varies inversely with x and y = 9 when x = 2. Write an equation for the inverse variation.

Is the relationship between the values in each table a direct variation, inverse variation, or neither? Is the relationship between the values in each table a direct variation, inverse variation, or neither? xy xy xy