PPT-Direct and Inverse Variation

SOL A8 by Robert Lotze Moody Middle School Direct Variation The longer you shower the more water you use You can describe this Relationship using Direct Variation The Direct Variation . Lesson 11-6. An equation in the form of ____________________ or . ____________ . is an inverse variation,. The constant of variation is _______, the _______________ of . . x. . and . y. for an ordered pair (x, y) that solves the inverse variation.. Lesson 3.08 . packet. . http://www.virtualnerd.com/algebra-1/linear-equation-analysis/direct-variation/direct-variation-definition/constant-of-variation-definition. . Per 3: Extra Credit for no missing assignments. Determine the asymptotes for:. Lesson . 3-8 . Direct, Inverse & Joint Variation. Objective: To recognize and use direct variation to solve problems. Definition:. . Y. varies directly as . x. means that . Goal: Use inverse variation and joint variation models.. Warm-up. Simplify:. Inverse Variation. 2 variables, x and y, vary inversely if:. k is called the constant of variation.. Example 1. Tell whether x and y show direct variation, inverse variation, or neither:. A direct variation is represented by a ratio or equation :. or. k ≠ 0. Direct Variation – constant ratio. EX1). x. 1. 2. 3. 4. y. 3. 6. 9. 12. Determine if the table represents a direct variation. If so, state the constant of proportionality. Section 5-2. Goals. Goal. To write and graph an equation of a direct variation.. Rubric. Level 1 – Know the goals.. Level 2 – Fully understand the goals.. Level 3 – Use the goals to solve simple problems.. Inverse variation. Recall: variables . x . and . y. show direct variation if . for some nonzero constant . a. .. *Note: the general equation . for inverse variation can be rewritten as . ..  . Classifying direct/inverse variation. Variation. What’s the Difference. Direct Variation. When we talk about a direct variation, we are talking about a relationship where as . x increases, . y increases. . or . decreases at a . CONSTANT. When a problem states that variable X varies directly as variable Y, we know that the relationship implied is . . X = . kY. And that the first step in solving the problem is to find the value of the constant of proportionality k. . Direct Variation. When we talk about a direct variation, we are talking about a relationship where as . x increases, . y increases. . or decreases at a . CONSTANT. . RATE. .. Direct Variation. Direct variation uses the following formula:. Direct Variation. y varies directly as x if there is a nonzero constant, k, such that . y = . kx. *k is called the constant of variation. Plug in the two values you have and solve for the missing variable. Investigation #1. Ramp height and length . vs. time. Direct . vs. Inverse. “. y. . varies . directly as . x. " . means… . y = . kx. . What does that graph look like?. “. y. . varies inversely as . y = . kx. , where k ≠ 0. . The constant of variation for a direct variation . k. is the coefficient of . x.. Example of direct variation. : The time it takes to hear thunder varies directly with the distance from lightning. (As the distance from lightning increases, so does the time it takes you to hear the thunder!). SOL A.8. Slope and Constant Of Variation. Constant of Variation and Slope are the same thing!!!. Slope Formula. . m=.  . What is the slope of a line passing through (0,0) and (4,1).. m=. = . = .