9.1 Inverse & Joint Variation
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9.1 Inverse & Joint 9.1 Inverse & Joint Variation Variation p.534 p.534 What is direct variation? What is direct variation? What is inverse variation? What is inverse variation? What is joint variation? What is joint variation?
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9.1 Inverse & Joint Variation. p.534 What is direct variation? What is inverse variation? What is joint variation?. Just a reminder from chapter 2. Direct Variation Use y=kx. Means “y varies directly with x.” k is called the constant of variation. New stuff!. Inverse Variation - PowerPoint PPT Presentation
Transcript of 9.1 Inverse & Joint Variation
9.1 Inverse & Joint Variation9.1 Inverse & Joint Variation
p.534p.534
What is direct variation?What is direct variation?
What is inverse variation?What is inverse variation?
What is joint variation?What is joint variation?
Just a reminder from chapter 2Just a reminder from chapter 2
Direct Variation
Use y=kx.
Means “y varies directlyvaries directly with x.”
k is called the constant of variationconstant of variation.
New stuff!
Inverse VariationInverse Variation
“y varies inverselyvaries inversely with x.”
k is the constant of variationconstant of variation.
x
ky
Ex: tell whether x & y show direct variation, inverse variation, or neither.
a. xy=4.8
b. y=x+4
c. 5.1
yx
Hint: Solve the equation for y and take notice of
the relationship.
xy
8.4
Inverse Variation
Neither
xy 5.1
Direct Variation
Ex: The variables x & y vary inversely, and y=8 when x=3.
• Write an equation that relates x & y.
k=24• Find y when x= -4.
y= -6
x
kyuse :
38
k
x
ky
xy
24
4
24
y
Joint Variation
• When a quantity varies directly as the product of 2 or more other quantities.
• For example: if z varies jointly with x & y, then z=kxy.
• Ex: if y varies inversely with the square of x, then y=k/x2.
• Ex: if z varies directly with y and inversely with x, then z=ky/x.
Examples: Write an equation.
• y varies directly with x and inversely with z2.
• y varies inversely with x3.
• y varies directly with x2 and inversely with z.
• z varies jointly with x2 and y.
• y varies inversely with x and z.
2z
kxy
3x
ky
z
kxy
2
ykxz 2
xz
ky
• What is direct variation?What is direct variation?
y varies directly with x (y = kx)y varies directly with x (y = kx)
• What is inverse variation?What is inverse variation?
y varies inversely with x (y = k/x)y varies inversely with x (y = k/x)
• What is joint variation?What is joint variation?
A quantity varies directly as the product of A quantity varies directly as the product of two or more other quantities ( y = kxy)two or more other quantities ( y = kxy)
AssignmentAssignment
p. 537p. 537
21-33,21-33,
39-4339-43
