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

2. 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.

3. 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.

4. 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.

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

6. Checkpoint Graph the equation. ANSWER Graph a Direct Variation Equation 4x4xy = – 3. 4. 3 2 y x =

7. 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

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

9. 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. 30.6 = 5 153 30.5 = 10 305 30.1 = 20 602 30.27 15 454 ≈ 30.28 25 757 ≈ Words, y 305 15 454 20 602 25 757 Lines, x 510 153

10. 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. ==

11. 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

13. Homework