Page 433 - Algebra 1

L E S S O N Identifying, Writing, and Graphing
64
Inverse Variation
Warm Up
New Concepts
1. Vocabulary A(n) “undoes” another operation. (19)
Suppose y varies directly as x. Find the constant of variation. 2. y = 7x 3. -4y = 12x
(56) (56)
Write an equation of the direct variation that includes the given point. 4. (3, 9) 5. (-8, 4)
(56) (56)
Recall that direct variation occurs between two variables if y = kx and k ≠ 0.
Another type of variation, called inverse variation, may occur between two
variables. Inverse variation is a relationship between two variables whose
product is a constant. The equation xy = k or y = _k , where k is a nonzero x
constant, defines an inverse variation between x and y. The variable y is said to vary inversely with x.
Exploration Modeling Inverse Variation
One example of inverse variation is the relationship between the length and
width of a rectangle with a constant area.
a. Draw a rectangle that has a width of 1 unit and a length of 16 units on grid paper.
Continue to draw different
rectangles with an area of 16 square units, changing the length and width for each.
b. Copy and complete the table after drawing each rectangle.
Math Language
The letter k represents the constant of variation.
Width (x)
Length (y)
Area (xy)
1
16
16
16
16
16
16
Online Connection www.SaxonMathResources.com
c. What happens to the length of each rectangle as the width increases?
d. What will the product xy always equal?
e. Write an equation solved for y showing this relationship.
418 Saxon Algebra 1