Direct Variation

Direct Variation

Direct Variation.

Direct Variation

Direct variation describes a simple relationship between two variables . We say y varies directly with x if: y=kx. for some constant k , called the constant of variation or constant of proportionality .

Direct Variation

The Graph of a Direct Variation will graph a straight line that will pass through the origin. The slope can be positive or negative. The slope of the line will equal the constant of variation.

Multiple Choice

Which of the given graphs is a direct variation?

• A

• B

• C

• D

Multiple Choice

Is this a direct variation?

• yes

• no

Multiple Choice

Direct Variation?

• yes

• no

Multiple Choice

Is the given table a direct variation? If so, what is the constant of variation?

(in a direct variation - if x increases, then y also increases - proportionally. If x decreases, then y also decreases - proportionally)

• Yes; 1/3

• Yes; 3

• Yes; 5

• No

Multiple Choice

Which graph shows a proportional relationship between x and y?

• A
• B
• C
• D

Direct Variation

Using Tables

Multiple Choice

Write the equation for the table given.

• y = 1/3x
• y = 3x
• y = 1/2x

Multiple Choice

Which of the following is NOT a direct variation?

• y = -2x
• y = 1/2x
• 2x + 3y = 2
• 3y = 4x

Multiple Choice

Is the given table a direct variation? If so, what is the constant?

• Yes; 1/4
• Yes; 4
• Yes; 2
• No

Multiple Choice

Write an equation for this relationship.

• y = 4x
• y = 1/8x
• y = 1/4x
• y = 8x

Direct Variation

You can solve problems involving direct variation. Just Remember

y/x = y/x..

Multiple Choice

On a treasure map, the actual distance is directly related to the scaled distance.  If 15 miles is represented by 3 centimeters, then how many centimeters on the treasure map are equivalent to 135 miles?

• 27 cm
• 675 cm
• 529 cm
• 32 cm

Multiple Choice

In a direct variation, y = 39 when x = 3. 
Find the value of y when x = 2.

• 26
• 3
• 58.5
• 2

Multiple Choice

If y vaires directly with x and y= 12 when x= 15. What is the value of x when y= 16?

• 12.8
• 20
• 11.25
• 19

Multiple Choice

Trina's paycheck earnings varies directly as the number of hours she works. If she works 19 hours and earns $187.15, what should she earn if she worked 40 hours? 

• $394
• $440
• $472.80
• $512.20