Download F = 6 when x = 2, y = 9, and z = 3

1.10
Direct Variation
and
Inverse Variation
Direct Variation
y varies directly as x
y is directly proportional to x
y = kx
k is the constant of proportionality
Inverse Variation
y varies inversely as x
y is inversely proportional to x
k
y
x
Ex.
Find a mathematical model representing
the statement. Find k.
F is jointly proportional to x and the square root
of y and inversely proportional to the cube of z.
(F = 6 when x = 2, y = 9, and z = 3)
kx y
F
3
Z
 
k 2 9
6
3
3
Solve for k.
k 6
6
27
27 x y
F
3
z
k = 27
Now find F if x = 4, y = 16, and z = 4.
27  4  16
F
3
4
27
F
4
Finding a Least Squares Regression Line
The amount p (in millions of dollars)
of total annual prize money awarded
at the Indianapolis 500 race from 1995
to 2004 are shown in the table.
Construct a scatter plot that represents
the data and find the least squares
regression line for the data.
Year
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
Prize $, p
8.06
8.11
8.61
8.72
9.05
9.48
9.61
10.03
10.15
10.25
12
10
8
6
Prize $
4
2
0
0
5
10
15
Year (5 = 1995)
Come up with an equation that represents the points
by hand and by a graphing utility.
y - 8.6 = .243(x - 5) or
y = .243x + 6.785
y = .268t + 6.66
TI-86
Linear Regression
To input points
STAT
F2 (EDIT)
Type in data
There must be a one in the FSTAT column
Quit
a = y-int
To get best fit line
b = slope
STAT
Corr = corr
F1 (CALC)
coefficient
F3 (linR)
n = # of
Enter
ordered pairs
Gives you equation of best fit line
TI - 84
press STAT
arrow to calc
#4 LinReg(ax + b)
Press enter twice
a = slope
b = y-int