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Direct Variation

Direct Variation. Algebra I Mastery Cate Condon. The store you go into in the mall sells t-shirts. You are looking around and you see that 3 t-shirts cost $15 total. Given this information how much would 5 t-shirts cost?. We can set up a proportion: 3 5 15 c Cross multiply: 3c = 5*15= 75

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Direct Variation

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  1. Direct Variation Algebra I Mastery Cate Condon

  2. The store you go into in the mall sells t-shirts. You are looking around and you see that 3 t-shirts cost $15 total. Given this information how much would 5 t-shirts cost? • We can set up a proportion: 3 5 15 c • Cross multiply: 3c = 5*15= 75 3c = 75 c = 25 =

  3. 3c = 75 • We know that c is the variable. What does the c stand for or represent? • What is the 3 in front of the c called?

  4. 3c = 75 • We know that 3 is called the coefficient of the variable. • Another name for this is the constant of variation. • Why do you think that a number in front of variable is called a constant of variation?

  5. 10 = 2x  2x = 10 • For this equation, what is the variable and what is the constant of variation? • 3x = 1/6 • For this equation, what is the variable and what is the constant of variation?

  6. 10 = 2x • We can write this equation substituting variables: y = kx where k is the constant of variation and x and y are variables • We call this equation, y = kx, direct variation

  7. Direct Variation • A direct variation is a function in the form y = kx where k does not equal 0. • An equation is a direct variation if the equation can be written in the form y = kx.

  8. Is the Equation a Direct Variation?If it is, find the constant of variation. • -6x + 2y = 0 Want to see if the equation can be written like y=kx • Solve for y: 2y = 6x y = 3x • Yes it is a direct variation. • The constant of variation is 3

  9. Is the Equation a Direct Variation?If it is, find the constant of variation • 7y = 2x • Solve for y: y = (2/7) x • Yes it is a direct variation. • The constant of variation is (2/7)

  10. Try These • 0 = 10 + 3x • 8x = 4y • 6 + 9x = 2y

  11. Direct Variation • We say that y varies directly with x when we have the equation y = kx. • So if I say that p varies directly with z, what would our equation be? (keep k as our constant)

  12. Real World Example • Your distance from lightning varies directly with the time it takes you to hear thunder. If you hear thunder 10 seconds after you see the lightning, you are about 2 miles from the lightning. Write an equation for the relationship between time and distance.

  13. Real World Example • Your distance from lightning varies directly with the time it takes you to hear thunder: • y = distance from lightening • x = time it takes you to hear thunder

  14. Real World Example • y = kx • We know that y is 2 miles from the lightning (y = distance from lightening • We know that x is 10 seconds (x = time it takes you to hear thunder) • 2 = k(10)  solve for k • k = (2/10)=(1/5) • Our equation: y = (1/5)x

  15. Real World Example

  16. Real World Example

  17. Real World Example

  18. Real World ExampleTry This • A recipe for a dozen corn muffins calls for 1 cup of flower. The number of muffins varies directly with the amount of flour you use. Write a direct variation for the relationship between the number of cups of flour and the number of muffins

  19. Real World Example • y = kx • y = the number of muffins • x = amount of flour used • 12 = k(1)  12 = k • So our equation is y = 12x

  20. Closing • p varies directly with z. If p = 210 when z = 200, then write the formula for the relation between p and z. • Work by yourself on the notecard on your desk for the last 5 minutes.

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