Download 2.7 - Variation Direct Variation: Your wage: $8.25/hr Do you make

2.7 - Variation
Direct Variation:
Your wage: $8.25/hr
Do you make more $ when you work more hours?
HECK YEAH! This is an example of Direct Variation.
Direct Variation: y = kx
(k = constant of proportionality)
In English, this is read "y varies directly with x"
Example 1 : Write a general formula which describes
the following:
a. y varies directly with x; y = 84, x = 28
b. y varies directly with x²; y = 63, x = 6
.
Ex 2: The monthly payment (p) on a mortgage varies
directly with the amount borrowed (B). If the monthly
payment is $6.65 for every $1 000 borrowed:
(a) Find the formula which represents this.
(b) Find the monthly payment when the amount borrowed is
$1 20,000.
.
Inverse Variation:
You have a 2x4 piece of wood.
If the length of the piece of wood increases, can it hold
more weight or less?
LESS! This is an example of inverse variation.
Inverse Variation : y = k
x
In English, this is read "y varies inversely with x"
Example 3: Write a general formula which describes the
following variation:
a. y varies inversely with x; y = 6.5, x = 1 3
b. y varies inversely with x³; y = 4, x =
.
1
2
Ex 4: The maximum weight (W) that can be safely
supported by a piece of 2x4 varies inversely with its
length (l). Experiments show that a 1 0-foot long 2x4 can
support 500 lbs.
(a) Find the formula which represents this.
(b) Find the maximum weight that can be safely supported
by a 25 foot 2x4.
.
Joint Variation: When we have 2 or more variables
Combined Variation: When direct and inverse variation are
combined in some way
Example 5: The force (F) of the wind on a window varies
jointly with the area (A) of the window and the square of
the speed (v) of the wind. A wind of 30 mph blowing on a
4x5 window has a force of 1 50 lbs.
(a) Find the formula which represents this.
(b) What is the force on a 3x4 window caused by a
50 mph wind?
.