Bellringer Put your name at the top of the paper 1. Is the set {(2,0), (-1, 9), (4,-2), (3,0), (1,9)} a function? 2. Find the slope of the line that passes.

Slides:

Advertisements

Similar presentations

Section 3 Direct Variation

Advertisements

Learning Target Students will be able to: Identify, write, and graph direct variation.

Proportions  A proportion is an equation with a ratio on each side. It is a statement that two ratios are equal.  3 = 6 is an example of a proportion.

Chapter 5 Review.

Using Cross Products Lesson 6-4. Cross Products When you have a proportion (two equal ratios), then you have equivalent cross products. Find the cross.

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

Direct Variation Rhonda Yost. What is Direct Variation? A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation.

Warm Up Lesson Presentation Lesson Quiz.

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Direct Variation 5-4. Vocabulary Direct variation- a linear relationship between two variable that can be written in the form y = kx or k =, where k 

Warm-Up 2 1.Solve for y: 2x + y = 6 2.Solve for y: 2x + 3y = 0.

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.

5-4 Direct Variation Warm Up 1. Regina walked 9 miles in 3 hours. How many miles did she walk per hour? 2. To make 3 bowls of trail mix, Sandra needs 15.

2-3 D IRECT V ARIATION Objective: To write and interpret direct variation equations.

PRE-ALGEBRA. Lesson 8-4 Warm-Up PRE-ALGEBRA What is a “direct variation”? How do you find the constant, k, of a direct variation given a point on its.

Algebra 1 Section 4.2 Slope and Direct Variation.

Solving Proportions. 2 ways to solve proportions 1. Equivalent fractions (Old) Cross Products (New)

Direct Variation Warm Up Lesson Presentation Lesson Quiz

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

2.4 Writing Equations of Lines. We’ve learned to graph given an equation. Now we’ll learn to write the equation given the graph There are three ways.

Lesson 4-5 Warm-Up.

2.4 Writing Equations of Lines p. 91. Learning Target I can write equations of a line.

Variation Functions Essential Questions

Algebra1 Direct Variation

Direct Variation Section 1.9.

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

5-4 Direct Variation Warm Up Warm Up Lesson Presentation Lesson Presentation California Standards California StandardsPreview.

2.3 - Direct Variation.

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

The Circle Post-Lab II A ( cm 2 ) r ( cm ) Area vs. Radius A ( cm 2 ) r 2 ( cm 2 ) Area vs. Radius 2 Since the graph is linear and contains (0,0) Y-intercept.

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.

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.

5.5 Direct Variation Pg Math Pacing Slope Review.

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%

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

Ratio and Proportions Percents Direct and Inverse Variation.

Direct Variation Section 5-2. Goals Goal To write and graph an equation of a direct variation. Rubric Level 1 – Know the goals. Level 2 – Fully understand.

Write linear equations that represent direct variation

Direct Variation 5-5 Warm Up Lesson Presentation Lesson Quiz

Writing Linear Equations in Slope-Intercept Form

Direct Variation 5-6 Warm Up Lesson Presentation Lesson Quiz

Direct Variation.

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation Lesson 2-3.

Warm Up Solve each proportion. = = 1. b = y = 8 = = m = 52

Direct Variation Chapter 8 Section 8.9.

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

Model Direct Variation

Warm Up Solve for y y = 2x 2. 6x = 3y

Model Direct Variation

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

Lesson 5-2 Direct Variation

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

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Warm Up Solve for y y = 2x 2. 6x = 3y y = 2x – 3 y = 2x

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

2.3: Direct Variation If a man does not keep pace with his companions, perhaps it is because he hears a different drummer. Let him step to the music which.

Direct Variation Warm Up Lesson Presentation Lesson Quiz

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation Warm Up Lesson Presentation Lesson Quiz

Warm Up Solve for y y = 2x 2. 6x = 3y y = 2x – 3 y = 2x

ALGEBRA TWO Section Writing Equations of Lines

5.3 – direct variation Textbook pg. 301 Objective:

Learning Target Students will be able to: Identify, write, and graph direct variation.

5.5 Direct Variation Pg. 326.

Model Direct Variation

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Using Cross Products Chapter 3.

Presentation transcript:

Bellringer Put your name at the top of the paper 1. Is the set {(2,0), (-1, 9), (4,-2), (3,0), (1,9)} a function? 2. Find the slope of the line that passes through the following points, (9,4) and (3,2). 3. Write in standard form an equation of the line with slope -3 through the point (-2,6). 4. Write y = 7x – 2 in standard form. 5. What is the y-intercept of equation y = 2x +6?

2-3 Direct Variation M11.A.2.1.2: Solve problems using direct and inverse proportions M11.D.4.1.1: Match the graph of a given function to its table or equation

Objectives Writing and Interpreting a Direct Variation

Vocabulary A linear function defined by an equation of the form y = kx, where k ≠ 0, represents direct variation. When x and y are variables, you can write k =, so the ration y : x equals the constant k, the constant of variation.

Identifying Direct Variation From a Table For each function, determine whether y varies directly with x. If so, find the constant of variation and write the equation. x–1 2 5 y 3–615 a. Since the three ratios are not all equal, y does not vary directly with x. x 7 9–4 y1418–8 b. The constant of variation is 2. The equation is y = 2x. = and are both equal to –3, but = 3. yxyx 3 –1 – = 2, so y does vary directly with x. yxyx –8 –4 ===

Identifying Direct Variation From an Equation For each function, tell whether y varies directly with x. If so, find the constant of variation. a.3y = 7x + 7 Since you cannot write the equation in the form y = kx, y does not vary directly with x. b.5x = –2y 5x = –2y is equivalent to y = – x, so y varies directly with x The constant of variation is –. 5252

The perimeter of a square varies directly as the length of a side of the square. The formula P = 4s relates the perimeter to the length of a side. a.Find the constant of variation. The equation P = 4s has the form of a direct variation equation with k = 4. b.Find how long a side of the square must be for the perimeter to be 64 cm. P = 4sUse the direct variation. 64 = 4sSubstitute 64 for P. 16 = sSolve for s. The sides of the square must have length 16 cm. Real World Example

Suppose y varies directly with x, and y = 15 when x = 27. Find y when x = 18. Let (x 1, y 1 ) = (27, 15) and let (x 2, y 2 ) = (18, y). 15(18) = 27(y)Write the cross products. y = 10Simplify. Write a proportion. y1x1y1x1 y2x2y2x2 = Substitute. = y 18 y = Solve for y Using Proportion

Homework Pg 74 & 75 #1,2,9,10,17,18,23,24,25