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.

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.

Direct Variation Certain formulas occur so frequently in applied situations that they are given special names. Variation formulas show how one quantity.

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

9.1 Inverse & Joint Variation By: L. Keali’i Alicea.

3.4 – Slope & Direct Variation. Direct Variation:

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.

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.

College Algebra Sixth Edition James Stewart Lothar Redlin Saleem Watson.

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.

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

Warm up Determine the asymptotes for: 1. x=-2, x=0, y=1.

Variation Chapter 9.1. Direct Variation As x increases/decreases, y increases/decreases too. y = kx k is called the Constant of Variation k ≠ 0 “y varies.

Mathematical Modeling & Variation MATH Precalculus S. Rook.

Chapter 3.6 Variation. Direct Variation When one quantity is a constant multiple of another quantity, the two quantities are said to vary directly. For.

6.4 Objective: To solve direct and inverse problems.

9-4 Variation Direct Variation Inverse Variation Joint 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.

Precalculus Mathematics for Calculus Fifth Edition

Direct and Inverse Variation. Direct Variation Y varies directly to x, when x and y are related by the equation: y=kx. Here k is the constant of variation.

9.1 Inverse & Joint Variation p.534. Just a reminder from chapter 2 Direct Variation Use y=kx. Means “y v vv varies directly with x.” k is called the.

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

Lesson 6 & 7 Unit 5. Objectives Be able to find equations for direct variation: y = kx Be able to find equations for inverse variation: y = k/x Be able.

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.

1.11 Making Models Using Variation. 2 Objectives ► Direct Variation ► Inverse Variation ► Joint Variation.

Variation Functions Essential Questions

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,

Section Direct and Inverse Variation. Lesson Objective: Students will: Formally define and apply inverse and direct 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.

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

Section 1.6 Mathematical Modeling

3.8 Direct, Inverse, and Joint Variation

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:

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

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.

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.

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

Section 5.1 Direct, Inverse, and Joint 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, 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.

Direct and Inverse Variations

9.1 Inverse & Joint Variation

Variation Objectives: Construct a Model using Direct Variation

Joint Variation.

Inverse & Joint Variation

Model Inverse and Joint Variation

Direct and Inverse Variations

Direct and Inverse VARIATION Section 8.1.

3-8 Direct, Inverse, Joint Variation

Direct and Inverse Variations

5-2 Direct Variation.

8.1 Model Inverse & Joint Variation

Direct and Inverse Variations

8-5 Variation Functions Recognize and solve direct and joint variation problems. Recognize and solve inverse and combined variation problems.

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

Evaluating Algebraic Expressions

Direct Variation Two types of mathematical models occur so often that they are given special names. The first is called direct variation and occurs when.

Model Inverse and Joint Variation

9.1 Inverse & Joint Variation

Presentation transcript:

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 of x. To express a direct variation, we say that y varies directly as x. In other words, as x increases, y increases or decreases at a constant rate.

Ex1: a) If y varies directly as x and y=9 when x =-15, find y when x=21. Think of these as y 1, and x 1, Think of these as y 2, and x 2,

b) If y varies directly as x and y=-15 when x=5, find y when x=3. y 1, and x 1,

Ex 2) If y varies inversely as x and y=4 when x=12, find y when x=5. y 1, and x 1, y 2, and x 2,

b) If y varies inversely as x and y=-14 when x=12, find x when y=21.

Another type of variation is joint variation. This type of variation occurs when one quantity varies directly as the product of two or more other quantities.

Example 3: a)Suppose y varies jointly as x and z. Find y when x=8 and z=3, if y=16 when z=2 and x=5. Think of these as y 1, x 1, z 1 and these as y 2, z 2, x 2 Now plug into the formula and solve.

b) Suppose y varies jointly as x and z. Find y when x=10 and z=5, if y=12 when z=8 and x=3.

CLASSWORK 1.If y varies inversely as x and y = -12 when x = 5, find x when y = If y varies directly as x and y = 9 when x = 6, find y when x = Suppose y varies jointly as x and z. Find y when x = 5 and z = 3, if y = 18 when x = 3 and z = 5.