If $$y$$ varies directly with $$x$$ , how do you find $$k$$ ?

To find $$k$$ , use the formula $$k = \frac{y}{x}$$ , where $$y$$ is the value of the dependent variable and $$x$$ is the value of the independent variable.

If $$y = 14$$ when $$x = 6$$ , what is the constant of variation $$k$$ ?

Using the formula $$k = \frac{y}{x}$$ , we find $$k = \frac{14}{6} = \frac{7}{3}$$ .

What happens to $$y$$ if $$x$$ is doubled in a direct variation?

If $$x$$ is doubled, $$y$$ will also double, since they are directly proportional.

What is an example of a direct variation in real life?

An example of direct variation is the relationship between distance and time when traveling at a constant speed. If speed is constant, distance varies directly with time.

If $$y = 5$$ when $$x = 2$$ , what is the equation of the direct variation?

First, find $$k = \frac{y}{x} = \frac{5}{2}$$ . The equation is $$y = \frac{5}{2}x$$ .

What is the graph of a direct variation?

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

If $$y = 3x$$ , what is the constant of variation?

The constant of variation is $$k = 3$$ .

How do you determine if a relationship is a direct variation?

A relationship is a direct variation if the ratio of the two variables is constant for all pairs of values.

What is the significance of the origin in direct variation?

The origin (0, 0) is significant in direct variation because it indicates that when the independent variable is zero, the dependent variable is also zero.

If $$y = 10$$ when $$x = 5$$ , what is the value of $$k$$ ?

Using the formula $$k = \frac{y}{x}$$ , we find $$k = \frac{10}{5} = 2$$ .

Direct 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 the Direct Variation Equation?

Back

3.

FLASHCARD QUESTION

Front

What does the constant of variation represent in direct variation?

Back

4.

FLASHCARD QUESTION

Front

What is the ordered pair that a direct variation always passes through?

Back

A direct variation always passes through the origin, represented by the ordered pair (0, 0).

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

7.

FLASHCARD QUESTION

Front

How do you express a direct variation relationship mathematically?

Back

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