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Direct Variation Algebra I Mastery Cate Condon

Direct Variation

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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: 35 15c Cross multiply: 3c = 5*15= 75 - PowerPoint PPT Presentation

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Page 1: Direct Variation

Direct VariationAlgebra I Mastery

Cate Condon

Page 2: Direct Variation

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?

O We can set up a proportion:3 515 c

O Cross multiply:3c = 5*15= 753c = 75c = 25

=

Page 3: Direct Variation

O 3c = 75O We know that c is the variable. What

does the c stand for or represent?O What is the 3 in front of the c called?

Page 4: Direct Variation

O 3c = 75O We know that 3 is called the

coefficient of the variable.O Another name for this is the constant

of variation.O Why do you think that a number in

front of variable is called a constant of variation?

Page 5: Direct Variation

O 10 = 2x 2x = 10O For this equation, what is the

variable and what is the constant of variation?

O 3x = 1/6O For this equation, what is the

variable and what is the constant of variation?

Page 6: Direct Variation

O 10 = 2xO We can write this equation

substituting variables: y = kx where k is the constant of variation and x and y are variables

O We call this equation, y = kx, direct variation

Page 7: Direct Variation

Direct VariationO A direct variation is a function in the

form y = kx where k does not equal 0.

O An equation is a direct variation if the equation can be written in the form y = kx.

Page 8: Direct Variation

Is the Equation a Direct Variation?If it is, find the constant of variation.

O -6x + 2y = 0 Want to see if the equation can be written like y=kx

O Solve for y:2y = 6xy = 3x

O Yes it is a direct variation.O The constant of variation is 3

Page 9: Direct Variation

Is the Equation a Direct Variation?If it is, find the constant of variation

O 7y = 2xO Solve for y:

y = (2/7) x

O Yes it is a direct variation.O The constant of variation is (2/7)

Page 10: Direct Variation

Try TheseO 0 = 10 + 3xO 8x = 4yO 6 + 9x = 2y

Page 11: Direct Variation

Direct VariationO We say that y varies directly with x

when we have the equation y = kx.

O So if I say that p varies directly with z, what would our equation be? (keep k as our constant)

Page 12: Direct Variation

Real World ExampleO 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.

Page 13: Direct Variation

Real World ExampleO Your distance from lightning varies

directly with the time it takes you to hear thunder:

O y = distance from lighteningO x = time it takes you to hear thunder

Page 14: Direct Variation

Real World ExampleO y = kxO We know that y is 2 miles from the

lightning (y = distance from lighteningO We know that x is 10 seconds (x = time

it takes you to hear thunder)

O 2 = k(10) solve for kO k = (2/10)=(1/5)O Our equation: y = (1/5)x

Page 15: Direct Variation

Real World Example

y x kDV

equation

Case 1 2 10 1/5y =

(1/5)*10

Case 2 3 15 1/5y =

(1/5)*15

Case 3 4 20 1/5y =

(1/5)*20

Case 4 5 25 1/5y =

(1/5)*25

Page 16: Direct Variation

Real World Example

0.5 1 1.5 2 2.5 3 3.5 4 4.50

5

10

15

20

25

30

yxk

Page 17: Direct Variation

Real World Example

Page 18: Direct Variation

Real World ExampleTry This

O 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

Page 19: Direct Variation

Real World ExampleO y = kxO y = the number of muffinsO x = amount of flour used

O 12 = k(1) 12 = k

O So our equation is y = 12x

Page 20: Direct Variation

ClosingO p varies directly with z. If p = 210

when z = 200, then write the formula for the relation between p and z.

O Work by yourself on the notecard on your desk for the last 5 minutes.