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

18 questions

THE MERCHANT OF VENICE ACT 1

Flashcard

•

10th Grade

17 questions

Westward Expansion Review

Flashcard

•

9th Grade

17 questions

Physics Flashcard

Flashcard

•

9th Grade

12 questions

Data Transmission

Flashcard

•

9th Grade

10 questions

DNA Flashcards

Flashcard

•

9th - 12th Grade

10 questions

Mastering Linear Equations

Flashcard

•

9th Grade

10 questions

ReactJS Flashcards

Flashcard

•

KG

9 questions

matematika kelas xi

Flashcard

•

11th Grade

Popular Resources on Wayground

10 questions

5.P.1.3 Distance/Time Graphs

Quiz

•

5th Grade

10 questions

Fire Drill

Quiz

•

2nd - 5th Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

22 questions

School Wide Vocab Group 1 Master

Quiz

•

6th - 8th Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

20 questions

Inferences

Quiz

•

4th Grade

12 questions

What makes Nebraska's government unique?

Quiz

•

4th - 5th Grade

Discover more resources for Mathematics

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

10 questions

Factor Quadratic Expressions with Various Coefficients

Quiz

•

9th - 12th Grade

19 questions

Explore Probability Concepts

Quiz

•

7th - 12th Grade

43 questions

STAAR WEEK 1

Quiz

•

9th - 12th Grade

10 questions

Exploring Abiotic and Biotic Factors in Ecosystems

Interactive video

•

6th - 10th Grade

10 questions

Exploring Tree Diagrams in Probability

Interactive video

•

6th - 10th Grade

20 questions

Simple Probability

Quiz

•

10th Grade

11 questions

Solving Quadratic Equations by Factoring

Quiz

•

9th - 12th Grade