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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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Direct VariationAlgebra 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?
O We can set up a proportion:3 515 c
O Cross multiply:3c = 5*15= 753c = 75c = 25
=
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?
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?
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?
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
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.
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
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)
Try TheseO 0 = 10 + 3xO 8x = 4yO 6 + 9x = 2y
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)
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.
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
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
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
Real World Example
0.5 1 1.5 2 2.5 3 3.5 4 4.50
5
10
15
20
25
30
yxk
Real World Example
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
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
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.