Ch. 11Vocabulary 5) Inverse variation

Slides:

Advertisements

Similar presentations

Agenda Lesson 4-6 – Inverse Variation - Day 1 Standards 15.0 Use algebraic techniques Standards 16.0 Give pertinent information about given functions Warm.

Advertisements

Write and graph a direct variation equation.

EXAMPLE 2 Graph direct variation equations Graph the direct variation equation. a.a. y = x 2 3 y = –3x b.b. SOLUTION a.a. Plot a point at the origin. The.

Direct and Inverse Variation

Vocabulary direct variation constant of variation

Ch. 9.2 Graphing Inverse Variations

9.3 Graphing Quadratic Functions

12-1 Inverse Variation Warm Up Lesson Presentation Lesson Quiz

Lesson 4-6 Warm-Up.

Inverse Variation ALGEBRA 1 LESSON 8-10 (For help, go to Lesson 5-5.)

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

ALGEBRA READINESS LESSON 8-6 Warm Up Lesson 8-6 Warm-Up.

Inverse Variation. Vocabulary Inverse variation- a relationship between two variables that can be written in the form y =k/x or xy = k, where k is a nonzero.

Variation Functions Essential Questions

Direct Variation Section 1.9.

U SING D IRECT AND I NVERSE V ARIATION D IRECT V ARIATION The variables x and y vary directly if, for a constant k, k  0. y = kx, Objective Lesson 11.3.

Definitions of the Day (DODs)

I can write and graph an equation of a direct variation.

4.6 Model Direct Variation

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

12.1 Warm Up Warm Up Lesson Quiz Lesson Quiz Lesson Presentation Lesson Presentation Model Inverse Variation.

5-8 Extension: Inverse Variation Lesson Presentation Lesson Presentation.

U SING D IRECT AND I NVERSE V ARIATION D IRECT V ARIATION The variables x and y vary directly if, for a constant k, y x =k,k, k  0. or y = kx,

Inverse Variation. A relationship that can be written in the form y =, where k is a nonzero constant and x ≠ 0, is an inverse variation. The constant.

11-6 Inverse Variation. Problem 1: Writing an Equation Given a Point.

Using y = 8x, what is the value of x if y = 72? Complete the table of values for 4x = y X0123 Y.

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,

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.

Identify direct and inverse variation EXAMPLE 1 Tell whether the equation represents direct variation, inverse variation, or neither. a. xy = 4 SOLUTION.

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

Chapter 2: Linear Equations and Functions Section 2.1: Represent Relations and Functions.

Warm Up Solve each proportion The value of y varies directly with x, and y = – 6 when x = 3. Find y when x = – The value of y varies.

Holt Algebra Inverse Variation Entry Task Solve each proportion

Direct Variation Equations

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.

Definitions of the Day (DODs) 11.1 – Inverse Variation (Please have a calculator) Inverse Variation Constant Of Variation.

Algebra Direct, Joint, and Inverse Variation.

CHAPTER 4 REVIEW.

Rules for Graphing.

5.6 Inverse Variation Review

Direct Variation.

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

A relationship that can be written in the form y = , where k is a nonzero constant and x ≠ 0, is an inverse variation. The constant k is the constant.

A relationship that can be written in the form y = , where k is a nonzero constant and x ≠ 0, is an inverse variation. The constant k is the constant.

Inverse & Joint Variation

Direct Variation Chapter 8 Section 8.9.

Direct and Inverse Variation/Proportion

Model Inverse Variation

Model Direct Variation

5-2 Direct Variation.

Model Direct Variation

Vocabulary direct variation constant of variation

Inverse Variation.

Vocabulary direct variation constant of variation

Digital Lesson Graphs of Equations.

4.3 Graphing Equations of Lines From Intercepts

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

LESSON 12-1 INVERSE VARIATION

Notes Over 2.4 Writing an Equation Given the Slope and y-intercept

ALGEBRA TWO Section Writing Equations of Lines

5.3 – direct variation Textbook pg. 301 Objective:

5.5 Direct Variation Pg. 326.

Model Direct Variation

Is it proportional? We will look at some equations, graphs and tables and you will decide if the relationship is proportional. Tell why or why not. If.

Section 4.6 Direct Variation Direct Variation

The Graph of an Equation Objective: 1. Sketch graphs of equations 2. Find x- and y-intercepts of graphs of equations 3. Find equations of and sketch graphs.

Presentation transcript:

Ch. 11Vocabulary 5) Inverse variation 6.) constant of variation (for an inverse variation)

11-6A Inverse Variation Algebra 1

The variables x and y vary directly if, for a constant k, USING DIRECT AND INVERSE VARIATION DIRECT VARIATION The variables x and y vary directly if, for a constant k, y x = k, or y = kx, k  0.

The variables x and y vary inversely, if for a constant k, USING DIRECT AND INVERSE VARIATION INDIRECT VARIATION The variables x and y vary inversely, if for a constant k, k x = y, or xy = k, k  0.

MODELS FOR DIRECT AND INVERSE VARIATION USING DIRECT AND INVERSE VARIATION MODELS FOR DIRECT AND INVERSE VARIATION DIRECT VARIATION INVERSE VARIATION k x = y y = kx k > 0 k > 0

Example 1 When x is 3, y is 12. Find an equation that x and y vary inversely.

Example 2 Does the date in each table represent a direct variation or an inverse variation? For each, write an equation to model the data. A.) B.) x Y 4 -12 6 -8 8 -6 x y 4 -12 6 -18 8 -24

An 8 sliced pizza is share equally by a group of friends. Example 3 Tell whether each situation represents a direct variation or inverse variation. Explain your reasoning. An 8 sliced pizza is share equally by a group of friends.

Assignment

Example 3 Decide if the data in the table show direct or inverse variation. Write an equation that relates the variables. #37 on pg. 660

Compare the direct variation model and the inverse Comparing Direct and Inverse Variation Compare the direct variation model and the inverse variation model you just found using x = 1, 2, 3, and 4. SOLUTION Plot the points and then connect the points with a smooth curve. Direct Variation: the graph for this model is a line passing through the origin. Direct y = 2x Inverse Variation: The graph for this model is a curve that gets closer and closer to the x-axis as x increases and closer and closer to the y-axis as x gets close to 0. Inverse 8 x y =

Example 2 Make a table of values for x = 1, 2, 3 and 4. Use the table to sketch a graph. Decide whether x and y vary directly or inversely. #33 pg. 659

Compare the direct variation model and the inverse Comparing Direct and Inverse Variation Compare the direct variation model and the inverse variation model you just found using x = 1, 2, 3, and 4. Make a table using y = 2x and y = . 8 x SOLUTION 8 x y = y = 2x 1 2 3 4 6 Direct Variation: k > 0. As x increases by 1, y increases by 2. Inverse Variation: k > 0. As x doubles (from 1 to 2), y is halved (from 8 to 4).