1.10 Direct Variation and Inverse Variation Direct Variation

1.10 Direct Variation and Inverse Variation Direct Variation

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 k = 27 6= 27 27 x y F= 3 z 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

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