Direct Variation (Review)
Direct variation: two variable quantities that have a constant ratio.
y
= k → y = kx .
x
- k is the variation constant
* If y varies directly with x, then
Inverse Variation
Inverse variation: two variable quantities that have a constant product.
* If y varies inversely with x, then xy = k → y =
- k is the variation constant
k
.
x
Joint Variation
Joint variation: a quantity that varies directly as the product of two or
more variable quantities.
* If z varies jointly with x and y , then
-
z
= k → z = kxy .
xy
k is the variation constant
Examples: Do x and y show direct variation, inverse variation, or
neither.
1. xy = 4.8
y
3.
2. x =
1.5
20
17
12
x 31
y 217 140 119 84
Examples: Write an equation for each statement.
5. z varies jointly with x2 and y.
4. y varies inversely with x3.
6. The variables x and y vary
inversely. If x = 10 and y = 2, write
an equation relating x and y.
Then, find y when x = 4.
7. The variables z varies jointly
with x and y. If x = 4, y = 3, and
z = 24, write an equation that
relates x, y, and z. Then find z
when x = 2 and y = 9.
The following table represents Boyle’s Law for a sample of hydrogen
gas where P is the pressure (in atmospheres) of the gas and V is the
volume (in cubic liters) of the gas. Use the table to do the following.
P
1.5
2.4
4
5
8
V
8.56
5.35
3.21
2.568
1.605
8. Does the table show direct or
inverse variation?
9. Write an equation that relates P
and V.
10. Find the volume of the
hydrogen gas if the pressure is
changed to 1.2 atmospheres.
11. Write a statement about what
Boyle’s law states.