A.2D Write and solve equations involving Direct 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.

Direct Variation 5-2.

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.

Direct Variation.

To write and graph an equation of a direct variation

Tell whether the equation represents direct variation.

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

Write and graph a direct variation equation

Essential Question: What does the k represent in a direct variation?

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.

Determine whether (2, 4) is a solution for y= 5x-6.

Direct Variation Solve each equation for the given variable.

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.

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.

Notes Over 4.5 Writing a Direct Variation Equation In Exercises 1-6, the variable x and y vary directly. Use the given values to write an equation that.

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

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.

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.

I can write and graph an equation of a direct variation by identifying the constant of 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.

Inverse Variations Lesson 11-6.

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 4-6 Warm-Up.

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

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

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

Lesson 4-5 Warm-Up.

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

Algebra1 Direct Variation

Definitions of the Day (DODs)

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

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

Direct Variation 3.6. Direct Variation  Direct Variation is when two variables can be expressed as y=kx where k is a constant and k is not 0.  k is.

4.6 Model 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.

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.

5.2 Slope and Direct Variation What you’ll learn: 1.Write and graph direct variation equations. 2.To solve problems involving direct variation.

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.

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.

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

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.

Objective: Modeling variation.

Model Direct Variation

Warm Up Problem of the Day Lesson Presentation Lesson Quizzes.

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.

Direct Variation Lesson 2-3.

Math CC7/8 – April 24 Math Notebook: Things Needed Today (TNT):

Tables and Relations Review

5-2 Direct Variation What is Direct Variation?

Model Direct Variation

Tables and Relations Review

5-2 Direct Variation.

Model Direct Variation

Tables and Relations Review

Objectives Identify solutions of linear equations in two variables.

2.4 Writing Equations of Lines

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

7.2 Graphing Equations.

Model Direct Variation

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

Presentation transcript:

A.2D Write and solve equations involving Direct Variation

Concept Summary: Graphs of Direct Variations The graph of a direct variation equation y=kx is a line with the following properties. The line passes through (0,0) The slope of the line is k.

Problem 1 Does the equation represent a direct variation? If so, find the constant of variation. 7y=2x B. 3y + 4x = 8 The equation has the form y=kx, so the equation is a direct variation. Its constant of variation is 2/7. You cannot write the equation in the form y=kx. It is NOT a direct variation

Writing a Direct Variation Equation Suppose Y varies directly with x, and y= 35 when x = 5. What direct variation equation relates x and y? What is the value of y when x =9? Y=kx Start with the function form of a direct variation 35 = k(5) Substitute 5 for x and 35 for y. 7=k Divide each side by 5 to solve for k. Y = 7x write an equation. Substitute 7 for k in y=kx. The equation y = 7x relates x and y. When x=9, y=7(9), or 63.

Graphing Direct Variation Weight on Mars= 50lb Weight on Earth= 130lb Graphing Direct Variation Weight on Mars y varies directly with weight on Earth x. The weights of the science instruments onboard the Phoenix Mars Lander on Earth and Mars are shown. What is an equation that relates weight, in pounds, on Earth x and weight on Mars y? Y=kx Start with the function form of a direct variation 50=k(130) Substitute 130 for x and 50 for y. 0.38=k Divide each side by 130 to solve for k Y= 0.38k write the equation. The equation y=0.38k gives the approximate weight y on Mars, in pounds, of an object that weights x pounds on Earth.

What is the graph of the equation in Part A? X Y 0.38(0)=0 50 0.38(50)=19 100 0.38(100)=38 150 0.38(150)=57 200 0.38(200)=76

Writing a Direct Variation from a Table For the data in the table, does y vary directly with x? If it does, write an equation for the direct variation. X Y 4 6 8 12 10 15 X Y -2 3.2 1 2.4 4 1.6 Find y/x for each ordered pair

For the data in each table, tell whether y varies directly with x For the data in each table, tell whether y varies directly with x. If it does, write an equation for the direct variation. Check your answer by plotting the points from the table and sketching the line. X Y -6 9 1 -1.5 8 -12 X Y 3 5.4 7 12.6 12 21.6 X Y -2 1 3 6 8 11

Word Problems The amount of blood in a person’s body varies directly with body weight. A person who weights 160 lbs has about 4.6qt of blood. About how many quarts of blood are in the body of a 175-lb person? The distance d you bike varies directly with the amount of time t you bike. Suppose you bike 13.2 mi in 1.25h. What is an equation that relates d and t? what is the graph of the equation?

Determine whether each equation represents a direct variation Determine whether each equation represents a direct variation. If it does, find the constant of variation. 2y = 5x + 1 8x + 9y = 10 -12x = 6y y + 8 = -x -4 + 7x + 4 = 3y 0.7x – 1.4y = 0

Ordered Pairs The ordered pairs in each exercise are for the same direct variation. Find each missing value. (3,4) and (9, y) (1, y) and (1.5, -9) (-5,3) and (x, -4.8)