Inverse Variation

Inverse Variation

Two variables x and y show inverse variation if given

 $y=\frac{k}{x}$  , where  $x\ne0$  

Multiple Choice

Does the equation show an inverse variation? 

 $y=\frac{10}{x}$  

• yes 

• no

Multiple Choice

What kind of variation does this equation show?

y = 6x

• Inverse Variation

• Direct Variation

• Joint Variation

• No Variations

Multiple Choice

Given the following equation, identify the constant k.

 $y=\frac{54}{x}$  

• There is none

• y = k

• k = x

• k = 54

Multiple Choice

True or False:

Inverse Variation passes through the origin of a graph and Direct Variation does not.

• True

• False

Multiple Choice

Identify the table:

Direct, Inverse, Or neither?

• Direct

• Inverse

• I don't Know

Multiple Choice

Identify the table:

Direct, Inverse, Neither

• Direct

• Inverse

• Neither

Multiple Choice

Identify the table:

Direct, Inverse, Or neither?

• Direct

• Inverse

• I don't know

Multiple Select

Which represents a Direct Variation?  Check all that apply.

•  $y=3x$  
  

•  $y=\frac{3}{x}$  

•  $3y=x$  

•  $y=\frac{x}{3}$  

Multiple Choice

True or False:

An Inverse Variation is always a curve and a Direct Variation is always a line?

• True

• False

Multiple Choice

What type of variation does this graph represent?

• Direct

• Inverse

• Neither

Multiple Choice

What type of variation does this graph represent?

• Direct

• Inverse

• Neither

Identify an Inverse Variation from a Table

•  $y=\frac{k}{x}$  is our definition of inverse variation, that means that  $x\cdot y=k$  is also true.

• To find if a table of values describe an inverse variation, multiply the x and y values.

• If we get the same constant, then we have an inverse variation.

Multiple Choice

Write the equation for the table given.

• $y=\frac{1}{3}x$

• $y=\frac{48}{x}$

• $y=3x$

• $y=\frac{3}{x}$

Multiple Choice

What is the constant (k) in this inverse variation?

• 12

• 48

• 24

• Not enough information given

Multiple Choice

Is the given table a direct or inverse variation? What is the constant of variation?

• Direct, 12

• 
  

  Direct, $\frac{1}{12}$

• Inverse, 12

• Inverse, $\frac{1}{12}$

Multiple Choice

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

• 
  

  Yes, $\frac{1}{3}$

• Yes, 5

• Yes, 3

• No

Multiple Choice

Given that y varies inversely with x, if x =7 and y = 4, what is y when x = 2?

• 14

• 2

• 10

• -14

Multiple Choice

x and y vary inversely. Given (5, 20), what is the constant k?

• 4

• 25

• 5

• 100

Multiple Choice

The volume V of a gas kept at a constant - temperature varies inversely with the pressure p. If the pressure is 24 pounds per square inch, the volume is 15 cubic feet. What type of variation problem is this and which is the formula?

• Direct; $V=k\cdot p$
  

• Inverse; $V=\frac{k}{p}$

• Direct; $p=k\cdot V$

• Inverse; $p=\frac{k}{V}$

Multiple Choice

The amount of money spent at the gas station varies directly with the number of gallons purchased. When 11.5 gallons of gas were purchased the cost was $37.72. Write the equation?

• $37.72=k⋅11.5$

• $37.72=11.5\cdot k​$

• $m=3.28⋅g$

• $m=\frac{433.78}{g}$

Multiple Choice

The time to complete a project varies inversely with the number of employees. If 3 people can complete the project in 7 days, how long will it take 5 people?

• t = 4.2 days

• t = 21 days

• t = 5 days

• t = 3 days