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Direct and Inverse Variation Functions

Direct and Inverse Variation Functions. Learning Goal 4.3. Direct Variation. Two variables, x and y, vary directly if there is a nonzero number k such that y=kx Just because one quantity increases when the other increases does not mean x and y vary directly

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Direct and Inverse Variation Functions

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  1. Direct and Inverse VariationFunctions Learning Goal 4.3

  2. Direct Variation • Two variables, x and y, vary directly if there is a nonzero number k such that y=kx • Just because one quantity increases when the other increases does not mean x and y vary directly • When one quantity changes by the SAME factor as another, the 2 quantities are in direct proportion • “k” is the constant of proportionality (multiplier), as well as the slope of the linear function

  3. Inverse Variation • 2 variables, x and y, vary inversely if there is a non-zero number k such that y=k/x; OR xy = k • Just b/c 1 quantity decreases as the other increases does not mean the 2 quantities are inversely proportional • When one quantity always decreases by the SAME factor as the other increases, the 2 quantities are inversely proportional

  4. Direct Slope Output equals input times slope (m same as k) Form y = kx Direct proportion Both go up/both go down Inverse Slope Input times Output equal slope (m same as k) Form xy = k Inverse proportion One goes up, other goes down Side by Side Comparison

  5. Examples: Inverse or Direct? • Fred earns $6.50 per hour • Direct, y = 6.5x • Edwina Earns $450 plus 7.5% commission on sales • Neither: y = 450 + 0.75x • A car travels 250 miles to Myrtle Beach; the faster it goes, the less time the trips takes • Inverse: r x t = 250

  6. More Examples • For his flooring business, Joe needs to convert feet to yards • Direct: y = 3f • If the area of a rectangle remains constant and the width decreases, then the length increases • Inverse: A = lw • The volume of the water in a swimming pool as the water drains at a rate of 200 gallons per min. • Neither: Volume implies a 3rd dimension

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