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Section 2.2 – DIRECT Variation

Section 2.2 – DIRECT Variation. Some quantities are in a relationship where the ratio of corresponding values is constant. You can write a formula for a direct variation function as y = kx or y/x = k, where k CAN NOT equal 0, x represents input values, and y represents output values

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Section 2.2 – DIRECT Variation

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  1. Section 2.2 – DIRECT Variation Some quantities are in a relationship where the ratio of corresponding values is constant. You can write a formula for a direct variation function as y = kx or y/x = k, where k CAN NOT equal 0, x represents input values, and y represents output values The formula y/x = k says that, except (0,0), the ratio of all output-input pairs equals the constant k, the constant of variation.

  2. Section 2.2 – DIRECT Variation Problem 1: For each function, determine whether y varies directly with x. If so, what is the constant of variation and the function rule?

  3. Section 2.2 – DIRECT Variation Problem 1: For each function, determine whether y varies directly with x. If so, what is the constant of variation and the function rule?

  4. Section 2.2 – DIRECT Variation Problem 2: For each function, determine whether y varies directly with x. If so, what is the constant of variation? 3y = 7x 7y = 14x + 7 5x + 3y = 0 y = x/9

  5. Section 2.2 – DIRECT Variation In direct variation, y/x is the same for all pairs of data where x = 0. So is true for the ordered pairs (x1 ,y2) and (x2 ,y2) where neither x1 nor x2 is zero.

  6. Section 2.2 – DIRECT Variation Problem 3: Suppose y varies directly with x, and y = 9 when x = -15. What is y when x = 21?

  7. Section 2.2 – DIRECT Variation Problem 3: Suppose y varies directly with x, and y = 15 when x = 3. What is y when x = 12?

  8. Section 2.2 – DIRECT Variation Problem 4: A salesperson’s commission varies directly with sales. For $1000 in sales, the commission is $85. What is the commission for $2300 in sales?

  9. Section 2.2 – DIRECT Variation Problem 4: The number of Calories varies directly with the mass of cheese. If 50 grams of cheese contain 200 calories, how many calories are in 70 grams of cheese?

  10. Section 2.2 – DIRECT Variation Problem 4: If y2 varies directly with x2, does that mean that y must vary directly with x? Explain!

  11. Section 2.2 – DIRECT Variation Problem 5: What is the graph of each direct variation equation? a. y = -2x y = 3x

  12. Section 2.2 – DIRECT Variation

  13. Section 2.2 – DIRECT Variation

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