Direct Variation. A direct variation is… A linear equation The y-intercept must be zero!!!! The graph of a direct variation will ALWAYS go through the.

Slides:

Advertisements

Similar presentations

Vocabulary direct variation constant of variation.

Advertisements

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

Direct Variation 5-2.

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

To write and graph an equation of a direct variation

Direct Variation Equations

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

 A constant ratio in any proportional relationship  Really just another name for unit rate! Remember, to be constant means it never changes!

Warm Up Lesson Presentation Lesson Quiz.

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

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 

Slope. Direct Variation What you’ll learn To write and graph an equation of a direct variation. Direct variation and Constant of variation for a direct.

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

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

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

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.

3.6 Model Direct Variation

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.

Direct Variation Honors Math – Grade 8. Get Ready for the Lesson It costs $2.25 per ringtone that you download on your cell phone. If you graph the ordered.

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

Direct Variation Warm Up Lesson Presentation Lesson Quiz

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

Time (days)Distance (meters) The table shows the movement of a glacier over six days.

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.

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

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

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

Variation Functions Essential Questions

Algebra1 Direct Variation

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

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

Slope and Direct Variation Mr Smith. By the end of this…  You should know what direct variation is, why it is important, and how you could use it. 

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.

Direct Variation Chapter 5 Section 2. Objective  Students will write and graph an equation of a direct variation.

Warm UpOct. 15  For numbers 1-3, find the slope of the line that passes through each pair of points 1. (-4, -1) and (-3, -3) 2. (-2, 3) and (8, 3) 3.

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.

5.5 Direct Variation Pg Math Pacing Slope Review.

What do you guess?. # of hours you studyGrade in Math test 0 hour55% 1 hour65% 2 hours75% 3 hours95%

Warm Up Write down objective and homework in agenda Lay out homework (Graphical stories wkst) Homework (WB 5-5)

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

Lesson 88 Warm Up Pg Course 3 Lesson 88 Review of Proportional and Non- Proportional Relationships.

2.2 Constant Rates of Change

Direct Variation 5-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation.

Direct Variation 5-6 Warm Up Lesson Presentation Lesson Quiz

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

Model Direct Variation

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

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

5-2 Direct Variation.

Model Direct Variation

Algebra November 12, Direct Variation Objective:

Direct & Inverse Variation

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 Equations

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation Warm Up Lesson Presentation Lesson Quiz

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Direct Variation Equations

Direct Variation Warm Up Lesson Presentation Lesson Quiz

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

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

Section 4.6 Direct Variation Direct Variation

Direct Variation 4-5 Warm Up Lesson Presentation Lesson Quiz

Presentation transcript:

Direct Variation

A direct variation is… A linear equation The y-intercept must be zero!!!! The graph of a direct variation will ALWAYS go through the origin (0,0). In the equation, there will only be numbers with the variables (coefficients). The only other number used can be zero.

This is a direct variation…

Which is a direct variation? 1.y = 3x y = 2x 3.3x – y = 0 4.9x + 3y = x + 3y = 0 6.

Which is a direct variation?- Answers 1.y = 3x + 2no 2.y = 2xyes 3.3x – y = 0yes 4.9x + 3y = -3no 5.2x + 3y = 0yes 6. yes

Constant of Variation The constant of variation is the rate of change for the data that describes the variation (slope) The constant of variation is found by dividing “y” by “x” It is the slope of a linear equation whose y-intercept is zero!!!! “They” call it “k”. Y = kx

Equation of a Direct Variation y = kx

Suppose the ordered pair in each problem are for a direct variation. Write the equation of direct variation.

1.(2, 1) 2. (15, 12) 3. (6, 4) 4. (1.4, 2.8) 5.

Answers 1.(2, 1) y = 1/2x 2.(15, 12)y = 4/5x 3.(6, 4)y = 2/3x 4. (1.4, 2.8) y = 2x 5.y = -2x

Is this a direct variation? If so, write the equation. x y x y

Answers x y x y Yes; y = 1.8xNo

Write a direct variation for the following…

Example 1 The distance that you travel at a constant speed varies directly with the time spent traveling. It takes you 2 hours to travel 100 miles. Write an equation for the relationship between the time and distance. How far can you travel in 3.5 hours? How long will it take you to travel 400 miles?

Example 2 The money you earn varies directly with the number of lawns you mow. You earn $36 for mowing 3 lawns. Write an equation for the relationship between money earned and lawns mowed. How much money would you earn for mowing seven lawns? How many lawns did you mow for $60?

Try these… Tell whether each equation represents a direct variation. If so, identify the constant of variation. 1. 2y = 6x yes; x = 4y – 7 no Tell whether each relationship is a direct variation. Explain. 3.4.

Try These… Part II 5. The value of y varies directly with x, and y = –8 when x = 20. Find y when x = – Apples cost $0.80 per pound. The equation y = 0.8x describes the cost y of x pounds of apples. Graph this direct variation