Vocabulary
Inverse Variation- The relationship of two variables x and y if there is a nonzero number such as a such that y=a/x
Constant of Variation- The nonzero constant a in a direct variation equation y=ax, an inverse variation equation y=a/x, or a joint variation equation z=axy
Joint Variation- A relationship that occurs when a quantity varies directly with the product of two or more other quantities.
Constant of Variation- The nonzero constant a in a direct variation equation y=ax, an inverse variation equation y=a/x, or a joint variation equation z=axy
Joint Variation- A relationship that occurs when a quantity varies directly with the product of two or more other quantities.
Essential Information
Two variables x and y show direct variation if y=ax and a≠0.
y is said to vary directly with x.
Two variables show inverse variation if y=a/x and a≠0.
y is said to vary inversely with x.
In both kinds of variation, a is said to be the constant of variation
y is said to vary directly with x.
Two variables show inverse variation if y=a/x and a≠0.
y is said to vary inversely with x.
In both kinds of variation, a is said to be the constant of variation
Checking for Inverse Variation
The general equation y=a/x for inverse variation can be rewritten as xy=a This tells you that a set of data pairs (x,y) shows inverse variation if the products xy are constant or approximately constant.
The general equation y=a/x for inverse variation can be rewritten as xy=a This tells you that a set of data pairs (x,y) shows inverse variation if the products xy are constant or approximately constant.
Joint Variation
Joint variation occurs when a quantity varies directly with the product of two or more other quantities. a≠0
z=axy z varies jointly with x and y
p=aqrs p varies jointly with q, r, and s.
Joint variation occurs when a quantity varies directly with the product of two or more other quantities. a≠0
z=axy z varies jointly with x and y
p=aqrs p varies jointly with q, r, and s.
Compare different types of variation