A.8 Direct & Inverse Variation

A.8 Direct & Inverse Variation

By Jessica Bergan

​	​Direct Variation	​Inverse Variation
​	​y varies directly with x	​y varies inversely with x
​Formulas	​y=kx --> k=y/x	​y=k/x --> k=xy
​Given a table...	​Divide the y-value by the x-value	​Multipy the x-value by the y-value

​Direct & Inverse Variation

k is the constant of variation (#)​

​

​Direct Variation MUST go through the origin (0,0).

Multiple Choice

SOL Question: This relation is an inverse variation.

$$\left\{\left(-1,8\right),\ \left(4,-2\right),\ \left(-2,4\right)\right\}$$  

Which equation represents this relation?

• $$y=-3x+5$$  

• $$y=-2x$$  

• $$y=-\frac{x}{8}$$  

• $$y=-\frac{8}{x}$$  

Draw

SOL Question: The graph of the equation representing a direct variation passes through point A. Locate one additional point that is on the graph of this equation.

Draw

SOL Question: Point A is an element of a direct variation. Plot two points, other than A, that are elements of this direct variation. The coordinates of the points must be integers.

Multiple Choice

SOL Question: Two relationships are described.

Relationship S: Karen drove 160 miles in 4 hours, and then she drove 80 miles in 2 hours.

Relationship T: Vernon cooked 6 hamburgers in 10 minutes, and then he cooked 9 hamburgers in 15 minutes.

Which statement is true about these relationships?

• Neither relationship is direct variation

• Both relationships are direct variation

• Only relationship S is a direct variation

• Only relationship T is a direct variation

Multiple Choice

SOL Question: In which table does y vary directly with x?

Multiple Choice

SOL Question: Ms. Scott will pay $2,000 to have her house painted. The amount each painter earns, A, varies inversely for the number of painters, n, that will paint the house. Which equation best represents this situation?

• $$A=2,000+n$$  

• $$2,000=A+n$$  

• $$A=2,000n$$  

• $$2,000=An$$  

Multiple Choice

Label the equation as direct variation, an inverse variation, or neither direct nor indirect variation.

$$y=\frac{x}{60}$$  

• Direct Variation

• Inverse Variation

• Neither

Multiple Choice

Label the equation as direct variation, an inverse variation, or neither direct nor indirect variation.

$$x+y=60$$  

• Direct Variation

• Inverse Variation

• Neither

Multiple Choice

Label the equation as direct variation, an inverse variation, or neither direct nor indirect variation.

$$xy=60$$  

• Direct Variation

• Inverse Variation

• Neither

Multiple Choice

Label the equation as direct variation, an inverse variation, or neither direct nor indirect variation.

$$y=\frac{60}{x}$$  

• Direct Variation

• Inverse Variation

• Neither

Multiple Choice

Label the equation as direct variation, an inverse variation, or neither direct nor indirect variation.

$$y=60x$$  

• Direct Variation

• Inverse Variation

• Neither

Fill in the Blank

The points (- 4, 8) and (x, 2) are elements of an inverse variation. What is the value of x?

Multiple Choice

SOL Question: It takes Lucy 20 minutes to complete her homework at a rate of 2 problems per minute. Let y represent the total number of minutes it takes Lucy to complete her homework at a rate of x problems per minute. Which equation can be used to represent the relationship between x and y?

• $$y=10x$$  

• $$y=40x$$  

• $$y=\frac{10}{x}$$  

• $$y=\frac{40}{x}$$  

Multiple Select

SOL Question: The number of cakes sold varies directly with the number of people who attend a fair each day. If 200 cakes are sold when 3,000 people attend the fair, which two statements are true?

• The number of cakes sold is 80 when 7,500 people attend the fair.

• The number of cakes sold is 275 when 4,125 people attend the fair.

• The number of cakes sold is 300 when 2,000 people attend the fair.

• The number of cakes sold is 650 when 9,750 people attend the fair.