Direct Variation

Direct Variation

Direct Variation

A simple relationship between two variables when y changes directly with x (y = kx).

• When x increases, y increases

• When x decreases, y decreases​

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Direct Variation

How it changes is called the Constant of Proportionality (k).

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​y = 2x

(0,0)

(1,2)

(2,4)

(3,6​

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​y = 5x

(0,0)

(1,5)

(2,10)

(3,15)​

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​y = 1/2x

(0,0)

(1,1/2)

(2,1)

(3,1 1/2)​

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Multiple Choice

Which equation represents direct variation?

• y = kx

• y = x

• y2 - y1

• C = (3.14)d

Multiple Choice

What variable do we use to represent the Constant of Proportionality?

• k

• x

• t

• y

Direct Variation

How can we tell if an equation shows direct variation?

• Does the equation fit into y = kx​

• If not, solve for y and check.​

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​y = 4x y = 3x - 6 3y = 9x y + 2 = x - 6

Multiple Choice

Does the equation show direct variation?

y = -2x

• Yes

• No

• Depends

Multiple Choice

Does the equation show direct variation?

y - 3 = 9x

• Yes

• No

• Depends

Multiple Choice

Does the equation show direct variation?

2y = 8x

• Yes

• No

• Depends

Multiple Choice

Does the equation show direct variation?

5y = 15x - 5

• Yes

• No

• Depends

Direct Variation

How can we tell if a table shows direct variation?

• Is the table proportional?

• Can you find the Constant of Proportionality?​

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Multiple Choice

Is this table an example of Direct Variation?

• Yes

• No

• Sometimes

Multiple Choice

Is this table an example of Direct Variation?

• Yes

• No

• Sometimes

Multiple Choice

Is this table an example of Direct Variation?

• Yes

• No

• Sometimes

Multiple Choice

Is this table an example of Direct Variation?

• Yes

• No

• Sometimes

Multiple Choice

What is the Constant of Proportionality (k)?

• 2

• 3

• 6

• -3

Multiple Choice

What is the Constant of Proportionality (k)?

• 1

• 2

• 1/2

• 3.5

Direct Variation

How can we tell if a graph shows direct variation?

• Does it form a straigh line?

• Does it pass through the origin?​

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Multiple Choice

Does the graph show direct variation?

• Yes

• No

• Sometimes

Multiple Choice

Does the graph show direct variation?

• Yes

• No

• Sometimes

Multiple Choice

Does the graph show direct variation?

• Yes

• No

• Sometimes