# 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

## Recently Viewed Presentations

• Human Heredity Human Chromosomes A typical human body cell contains 46 chromosomes - 44 autosomes and 2 sex chromosomes Chromosomes are arranged in a karyotype, a picture of the chromosomes Human Heredity Human Heredity Males and females differ in the...
• HACER - Haz PONER - Pon SALIR - Sal TENER - Ten VENIR - Ven DECIR - Di IR - Ve SER - Sé VIN DIESEL HAS TEN WEAPONS *WITH ACCENT Follow SUBJUNCTIVE No + tú form of the present...
• For realists power comes before politics and influence and can be understood in material terms = Military, economic and strategic "capabilities" Modern realists emphasize the "Balance of Power" above all else 3) The Evolution of Realism: a) "Classical Realism": Carr...
• Probit model. The selection decision regarding whether to organize the process internally or to subcontract the work. Structural cost equations of the model. Estimate internal organization costs to correct for selectivity using an index constructed from the first-stage results.
• Since finishing the course I have pro actively arranged a few meetings or attended events that previously I would have been too scared to attend on my own. Retrospectively reading the 'fixed vs. growth mindset' article on the moodle site,...
• Sixth Grade. This is when students make the shift from learning to read, to reading to learn. ... Conditions for learning (based on the work of research of Brian Cambourne) Immersion-students are surrounded by a variety of books. Demonstrations-daily lessons.
• Electron transfer in condensed molecular systems ... molecules in STM junctions Electron transfer by hopping Molecular conduction Molecular Rectifiers Arieh Aviram and Mark A. Ratner IBM Thomas J. Watson Research Center, Yorktown Heights, New York 10598, USA Department of Chemistry,...
• Complete TM webquest. MARKET SEGMENTATION Dividing the entire market into smaller groups (of people) who share similar characteristics. Psychographic Geographic Behavioral Demographic DEMOGRAPHICS Segmenting the market based on personal characteristics such as age, gender, income, ethnic background, education and occupation.