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

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15 questions

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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

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