Chapter 8 Variation. 2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Relations between Changing Quantities In a fixed hour,

Slides:

Advertisements

Similar presentations

Lesson 12.1 Inverse Variation pg. 642

Advertisements

What You Will Learn Recognize and solve direct and joint variation problems Recognize and solve inverse variation problems.

Types of Variation Direct Variation: y varies directly as x. As x increases, y also increases. As x decreases, y also decreases. Equation for Direct.

Lesson 8-4: Direct, Joint, and Inverse Variation.

Identifying and Representing Proportional Relationships

What is it and how do I know when I see it?

Section 3.6 Variation. Direct Variation If a situation gives rise to a linear function f(x) = kx, or y = kx, where k is a positive constant, we say.

Variation. Direct Variation if there is some nonzero constant k such that k is called the constant of variation.

Chapter 1 Section 4. Direct Variation and Proportion Direct Variation: The variable y varies directly as x if there is a nonzero constant k such that.

Direct and Inverse Variation

Identify, write, and graph an equation of direct variation.

Constant of Proportionality

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

S2A Chapter 4 Simultaneous Equations Chung Tai Educational Press. All rights reserved. © Simultaneous Linear Equations in Two Unknowns  (  1)

LESSON 2.03: Direct & Partial Variation MFM1P 1) The total cost of bananas varies directly with the mass, in kilograms, bought. Bananas the mass, in.

Vocabulary direct variation constant of variation

Lesson 2.8, page 357 Modeling using Variation Objectives: To find equations of direct, inverse, and joint variation, and to solve applied problems involving.

Direct Variation Talking about the relationship between variables in a new way!!! Fun, Huh?

5-2 Direct Variation A direct variation is a relationship that can be represented by a function in the form y = kx, where k ≠ 0. The constant of variation.

 Direct Variation Function – A function that can be modeled with the equation y = kx.

Chapter 2 More on Functions Copyright ©2013, 2009, 2006, 2005 Pearson Education, Inc.

Direct Variation. A direct variation is… A linear equation The y-intercept must be zero!!!! The graph of a direct variation will ALWAYS go through the.

Variation Functions Essential Questions

Objective: Apply algebraic techniques to rate problems.

Problems of the Day 1.) Find the slope of the line that contains (–9, 8) and (5, –4). 2.)Find the value of r so that the line through (10, -3) and (r,

EQ: How can you recognize a direct variation equation? EQ: How can you recognize an inverse variation equation? a direct variation graph? an inverse variation.

1.11 Modeling Variation.

Direct Variation & Inverse Variation (SOL A.8) Chapters 5-2 & 11-6.

DIRECT VARIATION GOAL: WRITE AND GRAPH DIRECT VARIATION EQUATIONS Section 2-6:

5-4 Direct Variation Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day Lesson Quizzes Lesson Quizzes.

Section 1.6 Mathematical Modeling

LESSON 12-1 INVERSE VARIATION Algebra I Ms. Turk Algebra I Ms. Turk.

9-1 Notes. Direct Variation: Two variables, y and x, vary directly if: y = If k is any nonzero constant. Example: The equation: y = 5x exhibits direct.

Direct Variation y = kx. A direct variation is… A linear function Equation can be written in the form; y = mx ; m  0 ory = kx ; k  0 The y-intercept.

Writing a direct variation equation. write a direct variation problem when y = 20 and x = 10 y = kx 20 = k·10 k = 2 y = 2x.

3.8 – Direct, Inverse, and Joint Variation. Direct Variation When two variables are related in such a way that the ratio of their values remains constant.

Direct Variation 88 Warm Up Use the point-slope form of each equation to identify a point the line passes through and the slope of the line. 1. y – 3 =

What do you guess?. # of hours you studyGrade in Math test 0 hour55% 1 hour65% 2 hours75% 3 hours95%

Copyright © 2009 Pearson Education, Inc. Chapter 6 Section 5 – Slide 1 Chapter 4 Variation.

Inverse Variation Lesson 11-1 SOL A.8. Inverse Variation.

9.1: Inverse and Joint Variation Objectives: Students will be able to… Write and use inverse variation models Write and use joint variation models.

Direct and inverse variation

Notes Over 11.3 Using Direct and Inverse Variation When x is 4, y is 5. Find the equation that relates x and y in each case. Direct Variation Two quantities.

Direct Variation If two quantities vary directly, their relationship can be described as: y = kx where x and y are the two quantities and k is the constant.

Constant of Proportionality

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Advanced Math Topics Mrs. Mongold

Do - Now (-2, 1) & (4, 7) (1, 0) & (0, 4) (-3, -4) & (1, 6)

Chapter 8: Rational & Radical Functions

Algebra 1 Section 4.5 Solve direct variation problems

Constant of Proportionality

Model Inverse and Joint Variation

5-2 Direct Variation What is Direct Variation?

Inverse Variation Chapter 8 Section 8.10.

3-8 Direct, Inverse, Joint Variation

Joint Variation.

Vocabulary direct variation constant of variation

Inverse Variation.

What is it and how do I know when I see it?

Vocabulary direct variation constant of variation

Direct & Inverse Variation

The variables x and y vary directly if, for a constant k,

Linear Relationships Graphs that have straight lines

LESSON 12-1 INVERSE VARIATION

What is it and how do I know when I see it?

What is it and how do I know when I see it?

What is it and how do I know when I see it?

What is it and how do I know when I see it?

Direct Variation.

Model Inverse and Joint Variation

Presentation transcript:

Chapter 8 Variation

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Relations between Changing Quantities In a fixed hour, we go further if we ride faster.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation It takes less time to complete a 100 m race when we run faster. Relations between Changing Quantities

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Lighting up more bulbs can make the room brighter. Relations between Changing Quantities

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation We pay more if we travel a longer distance. Relations between Changing Quantities

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation With the same amount of money, we get less food if the price is higher. Relations between Changing Quantities

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation We experience certain relations among changing quantities in our daily life.  Speed   Distance   Speed   Time   Number of candles   Brightness   Distance   Fares   Price   Quantity bought  Relations between Changing Quantities

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (I)  x   y  and x   y  The meaning of y varies directly as x:  The value of keeps unchanged  Symbolically, y  x  In the form of equation, y  kx where k is a non-zero constant.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation The graph of equation y  kx is a straight line passing through the origin. Direct Variation (I)

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (II)  x 2   y  and x 2   y  The meaning of y varies directly as x 2 :  The value of keeps unchanged  Symbolically, y  x 2  In the form of equation, y  kx 2 where k is a non-zero constant.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Direct Variation (II) The graph of equation y  kx 2 is a curve.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation where u  x 2 Direct Variation (II) The graph of equation y  ku is a straight line passing through the origin.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation  x   y  and x   y   The value of xy keeps unchanged The meaning of y varies inversely as x:  Symbolically,  In the form of equation, or xy  k where k is a non-zero constant.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation The graph of equation is a curve.

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Inverse Variation The graph of equation y  ku is a straight line passing through (but does not include) the origin. Graph of y against u u where

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Joint Variation  If h is fixed, then y varies directly as r 2.  If r is fixed, then y varies directly as h.  Symbolically, y  hr 2  In the form of equation, y  khr 2 where k is a non-zero constant. The meaning of y varies jointly as h and r 2 :

2004 Chung Tai Educational Press © Chapter Examples Quit Chapter 8 Variation Partial Variation  y is the sum of two parts.  One part of y varies directly as h.  Other part of y varies directly as b.  In the form of equation, y  k 1 h  k 2 b where k 1 and k 2 are non-zero constants. The meaning of y partly varies directly as h and partly varies directly as b:

End