X36912 y1234 State whether the table shows a direct variation. Prove it in two ways. x46810 y5 1520 The variables x and y vary directly. Use the values.

Slides:

Advertisements

Similar presentations

2-3 Direct Variations.

Advertisements

Direct Variation 5-2.

Unit 7: Direct Proportion Direct Proportion Notes Ms. Shivertaker Lovinggood MS.

Equations of proportional relationships

Direct Variation Objective: Students will be able to identify, write and graph direct variation equation.

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.

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.

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

Warm Up Lesson Presentation Lesson Quiz.

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

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.

Language Goal  Students will be able to verbally express direct variation. Math Goal  Students will be able to identify, write, and graph direct variation.

5.5: Direct Variation. A function in the form y = kx, where k ≠ 0, is a direct variation. The constant of variation k is the coefficient of x. The variables.

Representing proportional relationships with equations.

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.

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.

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

Slopes and Direct Variation December 9, Review Slope Slope – Rise Run (-1, -4) and (2, 2)

Holt Algebra Direct Variation Use a graph of the function to find the value of f(x) when x = –4. Check your answer.

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

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)

Section 4.5 Direct Variation. What happens to Y as X goes up by 1?

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

2.3 - Direct Variation.

Warm Up 1) Find the slope of a line that goes through the points (-3, 5) and (11, -2) 2) Write the equation of a horizontal line that goes through the.

Problem of the Day At a concession stand, hamburgers are selling at a rate of 160 hamburgers per hour. The table shows the rate at which wraps are selling.

Direct Variation y = kx. A direct variation is… A linear function Equation can be written in the form; y = mx ; m  0 ory = kx ; k  0 The 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.

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%

Chapter 5 Review. Slope Slope = m = = y 2 – y 1 x 2 – x 1 Example: (4, 3) & (2, -1)

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.

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

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

5-2 Direct Variation What is Direct Variation?

Problem of the Day At a concession stand, hamburgers are selling at a rate of 160 hamburgers per hour. The table shows the rate at which wraps are selling.

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

5-2 Direct Variation.

Algebra November 12, Direct Variation Objective:

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

Direct Variation Direct Variation: y y

Objective Identify, write, and graph direct variation.

Solving Equations with Variables on Both Sides

Solving Equations with Variables on Both Sides

Old Thoughts…… Proportional relationships have a constant ratio, or unit rate. The graph of a proportional relationship is a straight line that passes.

Algebra Direct Variation.

LESSON 12-1 INVERSE VARIATION

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

5.3 – direct variation Textbook pg. 301 Objective:

Direct Variation.

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

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

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

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

1. How do I Solve Linear Equations

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

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

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

10/9/14: Section 3. 4 (not on Quiz tomorrow)

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

Presentation transcript:

x36912 y1234 State whether the table shows a direct variation. Prove it in two ways. x46810 y The variables x and y vary directly. Use the values of x and y to find a constant of proportionality. Then write an equation that relates x to y. y = 3 and x = 4

CoCo Puffs Marsh- mallows General Mills is coming out with a new cereal called Hot Cocoa. They experimented with some samples to decide their recipe. We will chart to samples What would the equation be?

Identifying Direct Variation Origin (0,0) Constant SLOPE Or check if the values form a proportion

If four Oreo cookies contain 220 calories. How many calories would be consumed if you eat three? Find the constant variation first. Write and use the equation to solve for three cookies.

The variables x and y vary directly. Use the values to find the constant of proportionality and write an equation that relates x and y. 9. y = kx K is for constant

xy If it goes through (0,0) The slope The change in y The change in x y = kx k =

xy Oh No! There is no 0! Oh No! There is no 0! xy Relax. We’ll make a space for one xy You try!

I wish everyone would go home and leave me alone! Rearranging Equations (Changing the Point-of-View) Solve for y: What is happening on the side with y? _______________________ What is the opposite? ______________________ x + y = 3

I wish everyone would go home and leave me alone! 4x + y = 7x

Can the equation be written y = kx? Only combine LIKE terms y = -4x y − 2x = x y − 5 = 5x + 2 y − 2 = 3x − 2 y + 3 = x xy = 5

Miles driven Gallons Gas used Is this a proportional relationship? Prove it in two ways