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Direct & Inverse Variations

Learn to recognize direct and inverse variation equations, compare their graphs, distinguish direct from linear equations, and understand the concept of constant rates in mathematics.

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Direct & Inverse Variations

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  1. Direct & Inverse Variations EQ: How can you recognize a direct variation equation? EQ: How can you recognize an inverse variation equation? a direct variation graph? an inverse variation graph?

  2. Direct Variations y = kx where k is the constant of variation Examples of direct variations: y = 2x y = 4x y = 1/2x y = -3x Consider this linear equation: y = 2x – 1 Compare a direct variation with the linear equation: What’s the difference? Y = 2x compared with y = 2x - 1

  3. Did you know… A direct variation can also be called a A direct proportion Some books / tests will say direct variation While others will say direct proportion. Be aware of both terms.

  4. Inverse Proportions Direct Proportions • Direct Variation • As x increases Y increases or decreases at a CONSTANT RATE • Inverse variation • As x increases, Y decreases (But the rate may not be constant).

  5. Compare the equations… Direct Inverse Y = kx Y = k/x Compare the graphs… Inverse variation graphs are curves that will never quite reach the axes. Direct variation graphs always go through the __________.

  6. Direct, Inverse, or neither? • Y = 2x • Y = 10/x • Y = -.5x • Y = 2x + 1 • Y = 3x – 8 • Y = 10x • Y = 12/x • Y = 13/x

  7. Now that you know the formula for direct and inverse, can you write the equation for each if given k? If x & y vary directly, write an equation if k = 4 Y = kx so, if k=4 ___________ If x & y vary directly, write an equation if k = 10 Y = kx so, if k=4 ___________ If x & y vary directly, write an equation if k = -3 Y = kx so, if k=4 ___________ If x & y vary INVERSELY, write an equation if k = 4 Y = k / x so, if k = 4 ___________ If x & y vary INVERSELY, write an equation if k = 10 Y = k / x so, if k = 4 ___________ If x & y vary INVERSELY, write an equation if k = -3 Y = k / x so, if k = 4 ___________

  8. Look at pages 314 & 315 in your book. • Read pg. 314 • Do pg. 315 • 1. k = Then graph it. 2. Missing width = ____ Now graph

  9. pg. 315 continued • 3. y = ____ Now graph it. • 4. Make an xy chart for Graph them here y = 1x y = 2x y = 3x

  10. Pg. 315 continued • 5. Write an inverse variation for k=30, k=20, and k=10 ________, ________, _________

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