# 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

• Stock Prices Soared. In 1920s, prices in the stock market kept rising. Speculation: Buying & selling of stocks in hope of making quick profit. Buying on Margin: Pay a small part of the stock's price as down payment, then borrow...
• Engaging in 'networking' (taking action to build career-related social networks) is a critical factor in career development (e.g. Wolff & Moser, 2009) and a core researcher competency (Vitae, 2010). Researchers report that 'doing networking' is a 'painful process'; a 'necessary...
• Cornucopians vs. NeoMalthusians. cornucopia, the mythical "horn of plenty" of the Greek mythology which supplied its owners with endless food and drink magically. a futurist who believes that continued progress and provision of material items for mankind can be met...
• Apresentação CliqueMusic é o maior portal e o maior banco de dados de informações biográficas e discográficas sobre a música brasileira de todos os gêneros (exceto o erud
• Mitosis Cell Division Timothy G. Standish, Ph. D. In The Beginning One Most of the organisms we see started out as one cell Humans start out as a single cell, the zygote, formed by uniting a sperm and egg The...
• AQA Unseen Poetry Lecture - Approaching poems - looking for Meaning. Unseen poetry is all about understanding the meaning and being able to make educated guesses about what the poet might have been trying to say and why they might...
• Implementation Of The SBAR Checklist To Improve Patient Safety In USAF Aeromedical Evacuation. Capt. Dana Adrian, Lt Col(s) KareyDufour, Capt. Scott Holcomb, ... Use Of SBAR Tool During Already Planned Military Training Event On 11 May 2011. ... PowerPoint Presentation
• Participate in league with Chaska, Eden Prairie, Edina, Carver, and Shakopee community teams under common rules. 12/13 practices and games will be at Bandimere, Lake Ann and Diethelm ... Edina, Jordan, and Shakopee community teams under common rules. 14/15 practices...