Direct Variation Unit Rate

9-4 Direct Variation

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A direct variation relationship is when the ratio of y to x is constant.

To find the value of k (or m) from a table of values, divide y by x.

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Sometimes the value of k is a fraction.

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Multiple Choice

Does this table of values show a direct variation relationship?

• Yes. $$8\div2,\ 12\div3,\ and\ 24\div6$$ all equal 4.

• No. $$12\div3$$ is not the same as $$2\div8$$ .

Multiple Choice

What is the value of k?

• $$5$$

• $$-5$$

• $$\frac{1}{5}$$

• $$-\frac{1}{5}$$

Multiple Choice

Does this table represent a direct variation relationship? If yes, what is the equation?

• Yes: $$y=5x$$

• No

• Yes: $$y=\frac{1}{5}x$$

• Yes: $$y=x+5$$

Multiple Choice

What is the value of k, the constant of variation?

• 3

• 1/3

• 1/2

• 2

Multiple Choice

Which equation represents this table?

• $$y=4x$$

• $$x=4y$$

• $$y=\frac{1}{4}x$$

• $$y=x+4$$

Math Response

This table represents a direct variation relationship. What is the missing value for "n"?

Type answer here

Correct Answer: 18

Deg^°

Rad

The graph of a direct variation relationship will always go through the origin.

Why is this true?

Multiple Choice

Does this graph show a direct variation relationship? If so, what is the equation?

• No

• Yes: $$y=60x$$

• Yes: $$y=\frac{1}{60}x$$

• Yes: $$x=60y$$

Multiple Choice

What is the equation for the red line?

• $$y=2x$$

• $$y=\frac{1}{2}x$$

• $$y=6x$$

• Not enough information

Multiple Choice

Does this graph represent a direct variation?

• No, it doesn't go through the origin.

• No, it has a positive slope.

• Yes, it's a straight line.

• Yes, it shows a linear function.

Multiple Choice

Does this graph represent a direct variation? If yes, what is the equation?

• No

• Yes: $$y=6x$$

• Yes: $$y=\frac{3}{2}x$$

• Yes: $$y=\frac{1}{6}x$$