Is the equation $$y = 2x$$ a direct variation?

Yes, it is a direct variation because it can be expressed in the form $$y = kx$$ with $$k = 2$$ .

What is the value of $$k$$ in the direct variation equation $$y = kx$$ if $$y = 10$$ when $$x = 5$$ ?

$$k = 2$$ , since $$10 = k(5)$$ leads to $$k = \frac{10}{5} = 2$$ .

If $$y$$ varies inversely with $$x$$ and $$y = 15$$ when $$x = 2$$ , what is $$k$$ ?

$$k = 30$$ , since $$y = \frac{k}{x}$$ gives $$15 = \frac{k}{2}$$ , leading to $$k = 15 \times 2 = 30$$ .

If $$y$$ varies directly with $$x$$ and $$y = 12$$ when $$x = 3$$ , what is $$y$$ when $$x = 6$$ ?

$$y = 24$$ , since $$k = 4$$ and $$y = kx$$ gives $$y = 4(6) = 24$$ .

What is the relationship between direct variation and proportionality?

Direct variation indicates that two quantities are proportional to each other, meaning as one increases, the other increases at a constant rate.

If $$y$$ varies inversely with $$x$$ and $$y = 5$$ when $$x = 4$$ , what is $$y$$ when $$x = 2$$ ?

$$y = 10$$ , since $$k = 20$$ and $$y = \frac{20}{x}$$ gives $$y = \frac{20}{2} = 10$$ .

What does the constant of variation represent in direct variation?

The constant of variation, $$k$$ , represents the rate at which $$y$$ changes with respect to $$x$$ in direct variation.

How can you identify a direct variation from a table of values?

If the ratio of $$y$$ to $$x$$ is constant for all pairs of values, then it represents direct variation.

What is the graph of a direct variation equation?

The graph of a direct variation equation is a straight line that passes through the origin (0, 0).

If $$y$$ varies directly with $$x$$ and $$y = 8$$ when $$x = 4$$ , what is $$y$$ when $$x = 10$$ ?

$$y = 20$$ , since $$k = 2$$ and $$y = kx$$ gives $$y = 2(10) = 20$$ .

What is the difference between direct and inverse variation?

Direct variation shows a constant ratio between two variables, while inverse variation shows a constant product between two variables.

Direct and inverse variation Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is direct variation?

Back

2.

FLASHCARD QUESTION

Front

What is inverse variation?

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

What ordered pair does a direct variation always go through when graphed?

Back

(0, 0), because direct variation passes through the origin.

7.

FLASHCARD QUESTION

Front

Which equation represents inverse variation?

Back

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

5 questions

Kuis statistika

Flashcard

•

11th Grade - University

11 questions

7517 05 Structured Programming

Flashcard

•

10th Grade - University

12 questions

Descriptive adjectives for Home and Furniture

Flashcard

•

10th Grade - University

12 questions

Organic 2 Exam 4 Review

Flashcard

•

KG

8 questions

CHILDREN 2 (1ST CLASS)

Flashcard

•

KG

15 questions

7517 01 Programming Basics

Flashcard

•

10th Grade - University

15 questions

Identify Aircraft as Military, Civilian and Cadet

Flashcard

•

KG - Professional Dev...

10 questions

Secondary storage

Flashcard

•

9th - 11th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

29 questions

Alg. 1 Section 5.1 Coordinate Plane

Quiz

•

9th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

11 questions

FOREST Effective communication

Lesson

•

KG

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

Discover more resources for Mathematics

20 questions

SSS/SAS

Quiz

•

9th - 12th Grade

14 questions

Making Inferences From Samples

Quiz

•

7th - 12th Grade

23 questions

CCG - CH8 Polygon angles and area Review

Quiz

•

9th - 12th Grade

15 questions

Module 3 Topic 1 Vocabulary Quiz

Quiz

•

10th Grade

20 questions

Domain and Range Spiral Review

Quiz

•

9th - 12th Grade

15 questions

Characteristics of Quadratics

Quiz

•

9th - 10th Grade

20 questions

Triangle Proportionality Theorem

Quiz

•

9th - 10th Grade

10 questions

Dividing a polynomial by a monomial

Quiz

•

10th - 12th Grade