EXAMPLE 5 Use a direct variation model a.a. Explain why C varies directly with s. b.b. Write a direct variation equation that relates s and C. ONLINE MUSIC.

Slides:

Advertisements

Similar presentations

EXAMPLE 1 Standardized Test Practice SOLUTION Substitute several values of h into the equation C = h and solve for C.Then identify the table that.

Advertisements

Interpolate using an equation EXAMPLE 1 CD SINGLES The table shows the total number of CD single shipped (in millions) by manufacturers for several years.

Write an equation in point-slope form

Example 1 Solve ax b c for x. Then use the solution to solve Solve a literal equation + = += 2x SOLUTION STEP 1 Solve ax b c for x. += ax b c Write.

Chapter Equations 1.6 Relations 1.7 Functions.

EXAMPLE 1 Identify arithmetic sequences

EXAMPLE 1 Solve absolute value inequalities

EXAMPLE 3 Write an equation for a function

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.

EXAMPLE 3 Solve a multi-step problem Many businesses pay website hosting companies to store and maintain the computer files that make up their websites.

EXAMPLE 2 Solve a matrix equation SOLUTION Begin by finding the inverse of A = Solve the matrix equation AX = B for the 2 × 2 matrix X. 2 –7 –1.

EXAMPLE 1 Multiplying Decimals decimal places + 2 decimal places 4 decimal places.

EXAMPLE 5 Solve a multi-step problem Recording Studio

Tell whether the equation represents direct variation.

EXAMPLE 7 Solve a multi-step problem Printing Costs You are creating brochures that promote your school’s sports events. You pay $20 for computer time.

EXAMPLE 1 Solving a Real-World Problem Music Club You pay $9.95 to join an Internet music club. You pay $.99 for each song that you download. Your cost.

EXAMPLE 4 Solve a multi-step problem CYCLING

Choose functions using sets of ordered pairs EXAMPLE 1 Use a graph to tell whether the ordered pairs represent a linear function, an exponential function,

EXAMPLE 1 Identify direct variation equations

Write a model using standard form EXAMPLE 6 Online Music You have $30 to spend on downloading songs for your digital music player. Company A charges $.79.

Write and graph a direct variation equation

SOLUTION EXAMPLE 2 Find the greatest common monomial factor Factor out the greatest common monomial factor. a. 12x + 42y a.a. The GCF of 12 and 42 is 6.

10.8 Warm Up Warm Up Lesson Presentation Lesson Presentation Compare Linear, Exponential, and Quadratic Models.

EXAMPLE 3 Solve a multi-step problem Many businesses pay website hosting companies to store and maintain the computer files that make up their websites.

Graph linear functions EXAMPLE 1 Graph the equation. Compare the graph with the graph of y = x. a.a. y = 2x b.b. y = x + 3 SOLUTION a.a. The graphs of.

2.4 Writing Equations for Linear Lines

4-6 Direct Variation Direct Variation: y = kx k=constant of variation = SLOPE Ex: y = 2x the constant of variation=2 All equations of form y=kx have.

Warm Up A shape has 5 faces, and 5 vertices how many edges does the shape have? A sphere has a radius of 7.5, what is its surface area and volume? What.

2.4 – Write Equations of Lines. Example 1: Write an equation of the line shown.

3.6 Model Direct Variation

SOLUTION Write an inverse variation equation EXAMPLE 5 x–5–34824 y2.44–3–1.5–0.5 Tell whether the table represents inverse variation. If so, write the.

Do Now Pass out calculators. You have about 10 minutes to work on your EOC Packet.

SOLUTION EXAMPLE 2 Divide a polynomial by a binomial Divide x 2 + 2x – 3 by x – 1. STEP 1 Divide the first term of x 2 + 2x – 3 by the first term of x.

EXAMPLE 1 Identify similar solids Tell whether the given right rectangular prism is similar to the right rectangular prism shown at the right. a. b.

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.

Inverse Variations Lesson 11-6.

Write and apply a model for direct variation EXAMPLE 2 Meteorology Hailstones form when strong updrafts support ice particles high in clouds, where water.

Warm Up #4 1. Write 15x2 + 6x = 14x2 – 12 in standard form. ANSWER

Lesson: 3.6 Model Direct Variation Essential Question: How do you write and graph direct variation equation? Warm-up: Rewrite the equation so.

Then/Now You found rates of change of linear functions. (Lesson 3–3) Write and graph direct variation equations. Solve problems involving direct variation.

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

4.6 Model Direct Variation

SOLUTION EXAMPLE 1 Represent relations Consider the relation given by the ordered pair (–2, –3), (–1, 1), (1, 3), (2, –2), and (3, 1). a. Identify the.

Write and apply a model for direct variation EXAMPLE 2 Meteorology Hailstones form when strong updrafts support ice particles high in clouds, where water.

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

EXAMPLE 2 Plot points in a coordinate plane

GUIDED PRACTICE for Example – – 2 12 – 4 – 6 A = Use a graphing calculator to find the inverse of the matrix A. Check the result by showing.

SOLUTION EXAMPLE 3 Write an equation of a line Write an equation of the specified line. The y- coordinate of the given point on the blue line is –4. This.

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

Aim #7.1: What is the difference between direct and inverse variation? The equation y =ax represents direct variation between x and y. Y is said to vary.

SOLUTION EXAMPLE 2 Find the greatest common monomial factor Factor out the greatest common monomial factor. a. 12x + 42y a.a. The GCF of 12 and 42 is 6.

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.

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

5.5 Direct Variation Pg Math Pacing Slope Review.

Lesson 5.2 Direct Variation Direct variation y = kx Where k is the constant of variation.

Warm-Up Exercises EXAMPLE 1 Standardized Test Practice What are the solutions of 3x 2 + 5x = 8? –1 and – A 8 3 B –1 and 8 3 C 1 and – 8 3 D 1 and 8 3 SOLUTION.

Warm-Up Exercises Lesson x – 2y = –8 2. –9x + 3y = 21 ANSWER y = 2x + 4 Rewrite the equation so y is a function of x. y = 3x + 7.

Lessons 8-5 to 8-10 and Graphing Inequalities

EXAMPLE 4 Check data for inverse variation

Ch. 11Vocabulary 5) Inverse variation

Model Direct Variation

Model Direct Variation

Day 76 – Review of Inverse Functions

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

12.1 Model Inverse Variation

Constant Rate of Change

Solutions of Linear Functions

5.5 Direct Variation Pg. 326.

Model Direct Variation

Presentation transcript:

EXAMPLE 5 Use a direct variation model a.a. Explain why C varies directly with s. b.b. Write a direct variation equation that relates s and C. ONLINE MUSIC The table shows the cost C of downloading s songs at an Internet music site.

SOLUTION EXAMPLE 5 Use a direct variation model Because the ratios all equal 0.99, C varies directly with s = == C s To explain why C varies directly with s, compare the ratios for all data pairs (s, C ): a.a. b.b. A direct variation equation is C = 0.99s.

EXAMPLE 5 Find a rate of change GUIDED PRACTICE for Example 5 7. WHAT IF? In Example 5, suppose the website charges a total of $1.99 for the first 5 songs you download and $.99 for each song after the first 5. Is it reasonable to use a direct variation model for this situation? Explain. ANSWER No; the equation that models this situation does not have the form y = ax.