Page 434 - Algebra 1

In a direct variation, y is equal to the product of the constant of variation
k and x; that is y = kx. However, in an inverse variation, y is equal to the
quotient of the constant of variation k and x; in other words, y = _k . x
Identifying an Inverse Variation
Tell whether each relationship is an inverse variation. Explain.
a. _y=x 6
SOLUTION
Example
1
Solve the equation for y. _y ·6=x·6
6
y = 6x This is a direct variation.
b. xy=5
SOLUTION
Solve the equation for y.
__ xy = 5
xx
y = _5 This is an inverse variation. x
For every ordered pair in an inverse variation, xy = k. This relationship can be used to find missing values in the relationship.
Using the Product Rule
If yvariesinverselyasxandy=3whenx=12,findxwheny=9. SOLUTION
Use the product rule for inverse variation.
Product Rule for Inverse Variation
If (x1, y1) and (x2, y2) are solutions of an inverse variation, then x1y1 = x2y2.
Example
2
Math Reasoning
Formulate Find the k-value and write an equation that could be used to find x.
x1y1 =x2y2 (12)(3) = x2(9)
36 = 9x2
4 = x2
When y = 9, x = 4.
Substitute the value 12 for x1, 3 for y1, and 9 for y2. Multiply.
Divide both sides by 9.
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