Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations. Key Words: direct variation constant of variation.

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Presentation transcript:

Lesson 2.6 Direct Variation Goal: Write and graph direct variation equations. Key Words: direct variation constant of variation

Direct Variation: Two variables x and y show direct variation, or vary directly, if y = kx where k is a nonzero constant called the constant of variation.

Example 1 Graph a Direct Variation Equation Graph. 4 7 y x= Find a second point by substituting a convenient value for x. 4 7 y x= Write equation. 4 7 y 4 = () Substitute 4 for x. SOLUTION Plot a point at the origin.

Example 1 Graph a Direct Variation Equation 7 y = Simplify. A second point is. 4, 7 () Plot the second point. Then draw a line through the two points as shown.

Checkpoint Graph the equation. ANSWER x y = 2 2. ANSWER Graph a Direct Variation Equation x – 1. y =

Checkpoint Graph the equation. ANSWER Graph a Direct Variation Equation 4x4xy = – y x =

Checkpoint The variables x and y vary directly. Write an equation that relates x and y. 5. x = 3,3, y = 9 – ANSWER y = 3x3x – 6. x = 10, y = 2 ANSWER = x 5 1 y Write a Direct Variation Equation

CHEFS create dishes and menus that will appeal to their customers. Executive chefs supervise kitchen operations and food service staff.

Example 3 Identify Direct Variation Tell whether the data, the numbers of words y in the first x lines of the Declaration of Independence, show direct variation. If so, write an equation relating x and y. SOLUTION Find the ratio of y to x for each data pair = = = ≈ ≈ Words, y Lines, x

Example 3 Identify Direct Variation The ratio of y to x in each pair is nearly the same, so the data show direct variation. Substituting 30.3 for k in y kx gives the direct variation equation y 30.3x. ==

Checkpoint 7. Tell whether the data show direct variation. If so, write an equation relating x and y. ( ),), 1, 2 ( ),), 2, 4 ( ),), 3, 8 ( ),), 4, 14 () 5, 22 ANSWER not direct variation Identify Direct Variation

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