Algebra I
description
Transcript of Algebra I
Algebra IAlgebra I4.6 4.6
Model Direct VariationModel Direct Variation
VocabularyVocabulary
• Constant of Variation:Constant of Variation: the number the number by which x and y are relatedby which x and y are related
• Direct Variation:Direct Variation: When y = kx and When y = kx and k does not equal zerok does not equal zero
EXAMPLE 1
Tell whether the equation represents direct variation. If so, identify the constant of variation.
2x – 3y = 0a. – x + y = 4b.
Yes; y = 2/3x so k = 2/3 NO
GUIDED PRACTICE
Tell whether the equation represents direct variation. If so, identify the constant of variation.
1. – x + y = 1
2. 2x + y = 0
3. 4x – 5y = 0
No; it does not vary directly.
Yes; it does vary directly.y = -2xConstant = -2
Yes; it does vary directly.y = 4/5xConstant = 4/5
EXAMPLE 2
Graph the direct variation equation.
a. y = x2 3
y = – 3xb.y
x
10
10
-10-10
y
x
10
10
-10-10
EXAMPLE 3
The graph of a direct variation equation is shown.
y = ax
2 = a (– 1)
Write the direct variation equation.a.Find the value of y when x = 30.b.
– 2 = a
So, the equation is y = -2x
Plug in 30 for xy = -2xy = -2 (30)
y = -60
GUIDED PRACTICE
4. Graph the direct variation equation.
y = 2x y
x
10
10
-10-10
Properties of Graphs of Direct Variation Equations
• The graph of a direct variation equation is a line through the origin.• The slope of the graph of y = ax is a.
GUIDED PRACTICE
y = ax
6 = a (4)
64a = 3
2=
5. The graph of a direct variation on equation passes through the point (4,6). Write the direct variation equation and find the value of y when x =24.
So, y = 3/2x
y = 3/2x
y = 3/2 (24)
y = 36
SALTWATER AQUARIUM
EXAMPLE 4
• Write a direct variation equation that relates w and s.• How many tablespoons of salt should be added
to a 30 gallon saltwater fish tank?
The number of tablespoons, s, of sea salt needed in a saltwater fish tank varies directly with the number of gallons of water, w, in the tank. A pet shop owner recommends adding 100 tablespoons of sea salt to a 20 gallon tank.
EXAMPLE 4
s = aw
100 = a(20)
5 = a
So, s = 5w
s = 5ws = 5 (30)s = 150
Therefore, 150 tablespoons of salt
are needed.
a. b.
EXAMPLE 5
a. Explain why C varies directlywith s.
b. Write a direct variation equation that relates s and C.
ONLINE MUSICThe table shows the cost C of downloading s songs at an Internet music site.
SOLUTION
EXAMPLE 5
Because the ratios all equal 0.99, C varies directly with s.
2.97 3 =
4.95 5
6.93 7= = 0.99.
Cs
To explain why C varies directly with s, compare the
ratios for all data pairs (s, C ):
a.
b. A direct variation equation is C = 0.99s.