8 1 Inverse Variation 2 2 Direct Variation
- Slides: 14
8. 1 Inverse Variation & 2. 2 Direct Variation Learning goals • recognize and use inverse variation • write and interpret direct variation equations • use joint and other variations
Inverse Variation: as x increases, y decreases So k = xy ‘k’ is the constant of variation
Direct Variation: as x increases, y increases a linear equation in the form y = kx where k cannot = 0
Ex 1 Find k Direct, inverse, or neither? x y 3 0. 7 6 0. 35 21 0. 1 Inverse Variation
Ex 2 Find k Direct, inverse, or neither? x y – 2 6 – 1. 3 5 7 – 4 neither
Ex 3 Find k Direct, inverse, or neither? x y – 2 5 4 – 10 6 – 15 Direct variation
Ex 4 Suppose that x and y vary inversely. If x = 7 and y = 4, write a function.
Ex 5 Are these direct variations? No Yes
Ex 6 A dripping faucet wastes a cup of water if it drips for three minutes. The amount of water wasted varies directly with the amount of time the faucet drips. Write an equation. How long must it drip to waste 4. 5 cups?
Combined Variations • y varies directly with the square of x: • y varies inversely with the cube of x: • z varies jointly with x and y and inversely with w: • z varies directly with x and inversely with the product of w and y:
Ex 7 The mass m of a moving object is related to its kinetic energy k and its velocity v by. Describe the relationship using a combined variation. M varies directly with k and inversely with the square of v
Ex 8 Describe the relationship using a combined variation. A varies directly with the product of b 1 plus b 2 and h
Ex 9 z varies directly as x and inversely as the square of y. When x = 35, y = 7, and z = 50, write a function and find z when x = 5 and y = 10.
WS 8. 1 & 2. 2 a Homework
- Direct and inverse variation graphs
- Direct variation constant of variation
- Inverse variation
- Direct variation examples with solution
- What does a direct variation graph look like
- What is the difference between direct and inverse variation
- How to calculate sst in regression
- Inverse variation graph examples
- What is an excluded value on a graph
- Why can't zero be in the domain of an inverse variation
- Inverse variation and the reciprocal function
- 8-5 variation functions
- What is it
- Inverse of a rational function
- Inverse variation