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.

Slides:

Advertisements

Similar presentations

Inverse, Joint, and Combined Variation

Advertisements

3.8 Direct, Inverse and Joint Variation

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

3.4-1 Variation. Many natural (physical) phenomena exhibit variation = one quantity (quantities) changing on account of another (or several) Principle.

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

9.1 Inverse & Joint Variation

9.5 = Variation Functions.

Variation Variation describes the relationship between two or more variables. Two variables, x and y, can vary directly or inversely. Three or more variables.

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

2.6 Scatter Diagrams. Scatter Diagrams A relation is a correspondence between two sets X is the independent variable Y is the dependent variable The purpose.

Direct and Inverse Variations Direct Variation When we talk about a direct variation, we are talking about a relationship where as x increases, y increases.

Rational Functions * Inverse/Direct

Notes Over 4.5 Writing a Direct Variation Equation In Exercises 1-6, the variable x and y vary directly. Use the given values to write an equation that.

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

Section 6Chapter 7. 1 Copyright © 2012, 2008, 2004 Pearson Education, Inc. Objectives Variation Write an equation expressing direct variation.

1 Algebra 2: Section 9.1 Inverse and Joint Variation.

Finding and Using Inverse Functions: Lesson 50. LESSON OBJECTIVE: 1)Recognize and solve direct and joint variation problems. 2)Recognize and solve inverse.

Do Now The ratio of men to women on a cruise is 6 to 8. If there are 168 people on the cruise, how many women are there?

College Algebra 3.6 Polynomial and Rational Inequalities 3.7 Variation.

LAST CHAPTER!!!!!!! Yay!!!!!!!!! 8.1 & 8.2 Direct, Inverse & Joint Variation.

Copyright © 2011 Pearson Education, Inc. Publishing as Prentice Hall.

2.7 Variation. Direct Variation Let x and y denote 2 quantities. Then y varies directly with x, or y is directly proportional to x, if there is a nonzero.

Direct Variation We say that two positive quantities x and y vary directly if an increase in one causes a proportional increase in the other. In this case,

Direct Variation Equation for direct variation:. Page 6 Steps: 1.Set up a proportion 2.Cross multiply and solve for variable Since x varies directly as.

1.11 Modeling Variation.

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

UNIT 2, LESSON 8 VARIATION. THREE TYPES OF VARIATION.

Warm Up Set up equations for each. 1. y varies directly with the square root of x 2. p varies inversely with the cube of m 3. g is proportional to the.

X = Y. Direct variation X 1 X = Y 1 Y 2.

Slide Copyright © 2009 Pearson Education, Inc. 6.5 Variation.

Joint and Combined Variation Review of Variations Direct Variation Inverse Variation Formula General Equation.

Section 1.6 Mathematical Modeling

8-1 Direct, Inverse, and Joint Variation Some relationships in mathematics can be described as examples of direct variation. This means that y is a multiple.

3.8 Direct, Inverse, and Joint Variation

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.

Algebra 2 Notes May 19, Warm-Ups Remembering Direct Variation If you need help remembering, refer to page 74 Example 4 y varies directly with x:

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.

Warm-up 4 th Hour – Honors Algebra II Chapter 7 Test Scores: 105, 104, 100, 98, 96, 94, 94, 90, 86, 86, 84, 78, 75, 73, 73, 65, 61, 61, 60, 60, 47, 41,

Wed 2/24 Lesson 8 – 1 Learning Objective: To find direct, inverse, & joint variations Hw: Lesson 8 – 1 & 2 – 2 WS.

Inverse Variation 2.5. In direct variation, if one variable increases, so does the other. Inverse variation is the opposite.

NOTES 2.3 & 9.1 Direct and Inverse Variation. Direct Variation A function in the form y = kx, where k is not 0 Constant of variation (k) is the coefficient.

8-1/2-2 DIRECT AND INVERSE VARIATION. Direct Variation Equation: y = kx Solve for constant “k” k = y/x As x increases, y increases As x decreases, y decreases.

9.1 Inverse Variation. Inverse variation When one value increases, the other decreases.

9.1 Inverse & Joint Variation p.534 What is direct variation? What is inverse variation? What is joint variation?

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

Section 3.5 Mathematical Modeling Objective(s): To learn direct, inverse and joint variations. To learn how to apply the variation equations to find the.

Proportionality. Direct Proportionality What is it? Direct proportionality is when one thing is directly proportional to another. Two quantities are in.

Direct Variation Equations

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, Inverse & Joint Variation Section 2.5. Direct Variation 2 variables X & Y show direct variation provided y = kx & k ≠ 0. The constant k is called.

Copyright 2013, 2009, 2005, 2002 Pearson, Education, Inc.

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.

how one quantity varies in relation to another quantity

Write linear equations that represent direct variation

Direct Variation.

Advanced Math Topics Mrs. Mongold

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

Chapter 8: Rational & Radical Functions

Chapter 7 Section 6.

Variation Objectives: Construct a Model using Direct Variation

Inverse & Joint Variation

Model Inverse and Joint Variation

2.3: Direct Variation Objective: Determine if a function is a direct variation function.

2.3: Direct Variation Objective: Determine if a function is a direct variation function.

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

Warm Up – August 14, 2017 Solve for y. 3 + y = 2x 6x = 3y

Model Inverse and Joint Variation

Chapter 1: Lesson 1.10 Mathematical Modeling & Relations

Presentation transcript:

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. “y varies directly as x” would simply mean as x increases – so does y. Or as x decreases – so does y. Form: y = kx n ; n > 0, k is nonzero k is called the constant of variation.

The variables x and y vary directly and y=15 when x=3. a) Write the equation relating x and y. b) Find y when x = 9.

The y varies directly as the cube of x and y=-67.5 when x=3. a) Write the equation relating x and y. b) Find x when y = -540.

Inverse Variation When the values of two quantities are related inversely proportional. As one value increases, the other value decreases and vice versa y = k/x n or x n y= k, n > 0

The variables x and y vary inversely when y = 14 when x = 3. a) Write the equation relating x and y. b) Find y when x = 9.

Suppose y varies inversely with x 2. When y = 15, x = 2. a) Write the equation relating x and y. b) Find y when x = 5.

Joint Variation A variation when one or more quantities vary directly as the product of two or more other quantities. y = kx n z n ; x and z are nonzero and n > 0

Example 1 If y varies jointly as x and the cube of z and y = 16 when x = 4 and z = 2, find y when x = -8 and z = -3

Example 2 If y varies jointly as x and z and inversely as the square of w, and y = 3 when x = 3, z = 10, and w = 2, find y when x = 4, z = 20, and w = 4.

Homework 3.8 page 194 # 15, 18, 20