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Direct Variation: Understanding and Applying the Concept

Learn how to identify and solve direct variation problems, find the variation constant, and apply these concepts to real-world situations. Practice exercises and quotes to inspire you.

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Direct Variation: Understanding and Applying the Concept

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  1. 2.3 Direct Variation “Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis “A smooth sea never made a skilled mariner.”-English Proverb

  2. KUDOs • Know-vocab Direct variation slope Variation constant Understand how to identify if a relationship is a direct variation. Understand how to find the variation constant given two points. Do-Identify if a function is a direct variation. Find the variation constant. Apply these concepts to solve real world situations.

  3. Warm up 1. What form is this equation in? Graph it. 2. What form is this equation in? Graph it. 2x – 4y = -8 • Y-3 = -2(x + 4)

  4. Direct Variation Direct Variation is y = kx The line passes through the origin, and k is the slope. How can y = kx be re-written to find k?

  5. Using a Table Does y vary directly with x in the following examples? 1. 2.

  6. Using Equations Does y vary directly with x in the following equations? • 4y = 24x • y = x - 2

  7. Water Conservation • A dripping faucet wastes a cup of water if it drips for 3 minutes. The amount of water wasted varies directly with the amount of time the faucet drips. • DTR (define the relationship) • Assign variables • Write an equation • Substitute the known values • Solve for the missing • Answer the question in a sentence.

  8. Water Conservation w = t How long does it take to waste 4.5 cups of water?

  9. Circumference Circumference varies directly with diameter. C = πd. What is our constant of variation (k)? What is the diameter when the circumference is 105 cm.?

  10. Using Proportions Suppose y varies directly with x, and x = 27 when y = -51. Find x when y = -17. Then find k. ***Discuss using cross-products!!

  11. 2.3 Direct Variation “Friendship is born at that moment when one person says to another, ‘What! You too? I thought I was the only one.’” -C. S. Lewis HW: # 1-19 odd, 23, 24-27, 33, 34, 46, 47 “A smooth sea never made a skilled mariner.”-English Proverb

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