1. Warm-up 4 th Hour – Honors Algebra II Chapter 7 Test Scores: 105, 104, 100, 98, 96, 94, 94, 90, 86, 86, 84, 78, 75, 73, 73, 65, 61, 61, 60, 60, 47, 41, 37, 16, 16 Find : Mean=_____Median=_____ Mode=_____Range=_____

2. Section 8-1 Model Inverse and Joint Variation

3. Vocabulary Direct Variation: y = ax Inverse Variation: y = a, a ≠ 0. x Joint Variation – A quantity varies directly with the product of two or more other quantities. z = axyz varies jointly with x and y. p = aqrsp varies jointly with q, r and s.

4. Example 1 Tell whether x and y show direct variation, inverse variation or neither. Rewritten Equation Type of Variation a.) y – 3x = 0 b.) x = 3 y c.) x + y = 5 Directy = 3x y = 3 x Equation cannot be written in the form y = ax Inverse Neither

5. Example 2 The variables x and y vary inversely, and y = 15 when x = 1 / 3. Write an equation that relates x and y. Then find y when x = -10. Step 1: Inverse form. 15 = a 1 / 3 y = a x a = 5 y = 5 x Step 2: Substitute 15 for y and 1 / 3 for x. Step 3: Solve for a. Step 4: Write the inverse variation. y = 5 -10 y = -½

6. Example 3 Determine whether x and y show direct variation, inverse variation or neither. Step 1: Calculate the product x y for each data pair in the table. 120050(24) = 100(12) = 120(10) = 150(8) = Each product is equal to 1200, so the data shows an inverse variation. y = 1200 x xy 5024 10012 12010 1508 1200

7. Example 4 The variable z varies jointly with x and y. Also, z = 60 when x = -4 and y = 5. Find z when x = 7 and y = 2. Step 1: Write the joint variation equation. 60 = a(-4)(5) z = axy 60 = -20a a = -3 Step 2: Find the constant of variation a. Step 3: Rewrite the joint variation equation. z = -3xy Step 4: Calculate z when x = 7 and y = 2. z = -3(7)(2) z = -42

8. Example 5 Write an equation for the given relationship. a.) r varies inversely with s. b.) z varies jointly with x and the square root of y. c.) p varies inversely with the cube of q. d.) m varies directly with the square of n and inversely with p. e.) z varies jointly with u and v and inversely with the square of w. r = a s m = an 2 p z = auv w 2 z = ax√ y p = a q 3

9. Homework Section 8-1 Pages 555 –556 1, 3 – 11, 13, 15, 20 – 22, 24 – 27, 31 – 33, 37, 38, 52 – 55