Remember: x and y show direct variation if y = kx for some nonzero constant k. Variables x and y show inverse variation if:k is called the constant of variation y is said to “vary inversely” with x
Totell whether x and y show direct or inverse variation:1. Rewrite by solving for y2. Check which pattern it followsExamples:
Dox and y show direct variation, inverse variation, or neither?
Use given values of x and y to find k. Then, write equation using form. Example: The variables x and y vary inversely, and y = 8 when x = 3. Write an equation that relates x and y. Find y when x = -4.
x and y vary inversely, and y = 6 when x = 1.5. Write an equation that relates x and y. Find y when x = 4/3
The inverse variation equation can be rewritten as xy = k. A set of data pairs (x, y) vary inversely if the products xy are approximately constant.Example: Does the data show inverse variation? If so, write a model relating x and y. x 3.6 5.0 6.3 4.0 2.8 y 32.5 23.5 18.7 29.2 42.2
Do these data show inverse variation? If so, find a model.w 2 4 6 8 10h 9 4.5 3 2.25 1.8
When a quantity varies directly as the product of two or more other quantities it is joint variation. If z = kxy where k ≠ 0, then z “varies jointly” with x and y.
Write an equation for each given relationship.a. y varies directly with xb. y varies inversely with xc. z varies jointly with x and yd. y varies inversely with the square of xe. z varies directly with y and inversely with x