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.

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Presentation transcript:

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.

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?

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?

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? a.3y = 7x b.7y = 14x + 7 c.5x + 3y = 0 d.y = x/9

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 (x 1,y 2 ) and (x 2,y 2 ) where neither x 1 nor x 2 is zero.

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?

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?

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?

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?

Section 2.2 – DIRECT Variation Problem 4: If y 2 varies directly with x 2, does that mean that y must vary directly with x? Explain!

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

Section 2.2 – DIRECT Variation