Direct and Inverse Variations

Sep 13, 2012

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Direct and Inverse Variations

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1. Direct and InverseVariations section 9-2

2. 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.

3. Direct Variation the gist of direct variation is the following formula:

Direct and Inverse Variations

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Direct and Inverse Variation. Investigation #1 Ramp height and length vs time. Direct vs Indirect. “ y varies directly as x " means… y = kx What does that graph look like? “ y varies inversely as x " means… y = k/x What does that graph look like? What is k?

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Direct and Inverse Variation. Algebra I. Direct Variation. When the line passes through the origin. When y increases, x increases. Equation: y = kx , where k 0. Constant of variation – k Say “ y varies directly with x”. Identifying the constant of variation. y = 6x

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Direct Variations. Vocabulary. Direct Variation When two variables form a constant ratio Equation: y = kx (where k is the constant ratio) Constant of variation The ratio k = y / x (note similarity to slope ratio). Direct Variation Identification. From a graph

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Inverse Variations . 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. xy =k. k. product.

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Inverse Variations

Inverse Variations. Unit 4 Day 8. Warm-Up Answers. Homework Answers. y = 7.25 ●x 1 Direct because x 1 6.25 miles y = 144 ●x -1 Inverse because x -1 2.4 people OR y = 144/x y = 9 ●x 1 Direct because x 1 111.1 hours Symmetry over y-axis

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Direct and Inverse Variations. Direct Variation. Which of these tables models direct variation? If so, write an equation. NO. Tell if the following graph is a Direct Variation or not. Yes (straight line through the origin!). No. No. No.

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DIRECT, INVERSE, AND JOINT VARIATION. Unit 3 English Casbarro. If y varies directly as x and y = 14, when x = 3.5, find k and write and graph the variation. Notice that the direct variation graph always intersects the coordinate plane at the origin. Try this: If y varies

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Graphing Inverse Variations. A relationship that can be written in the form y = k/x , where k is a nonzero constant and x ≠ 0, is an inverse variation . The constant k is the constant of variation .

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Presentation Transcript

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