Constant of Variation and Direct Variation

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 1/2

• yes, the constant of variation is 2

• no, there is constant of variation.

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• no, there is no constant of variation

• yes, the constant of variation is 100

• yes the constant of variation is 50

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 8.

• no, there is no constant of variation

• yes, the constant of variation is 1/8

Determine if the relationship between the two quantities is a direct variation. Explain your reasoning.

• yes, the constant of variation is 2

• yes, the constant of variation is 1/2

• no, there is no constant of variation

Determine if there is a constant of variation. If so, explain what it represents.

The equation y = 9.50 x represents the number of dollars y Marty paid for x movie tickets.

• The constant of variation is 9.50. This means that Marty paid $9.50 for each movie ticket

• There is no constant of variation. There is not a direct variation between the number of tickets and the total cost.

Determine if there is a constant of variation. If so, explain what it represents.

The equation y = 0.10 x + 45 represents the cost y of a cell phone plan when x text messages are sent and received.

• The constant of variation is $0.10. + 45. This means that for every text message sent, you pay 0.10 + $45.

• There is no constant of variation. The cost does not vary directly with the number text messages sent and received.

Determine if there is a constant of variation. If so, explain what it represents.

The equation y = 24 x represents the number of bottles of water y in x packages.

• The constant of variation is 24. This means that there are 24 bottles of water in each package.

• There is no constant of variation. The number of bottles varies per package.

Determine if the relationship between the two quantities is a direct variation.

• This is a direct variation since the graph passes through the origin and the ratio of the number of miles to the number of hours is constant.

• This is not a direct variation since the graph does not pass through the origin and the ratio of the number of miles to the number of hours is not constant.

• This s a direct variation since the graph is a straight line and the ratio of the number of miles to the number of hours is constant

• This is not a direct variation since the graph is not a straight line and the ratio of the number of miles to the number of hours is not constant.

The cost of paper varies directly with the number of reams bought. Suppose 2 reams cost $5.10. Write an equation that could be used to find the cost of x reams of paper.

• y= 5.10x

• y=2.55x + 2.55

• y = 2.55x

• 2.55y = x

Recall that the length a spring stretches varies directly with the amount of weight attached to it. A certain spring stretches 5 cm when a 10-gram weight is attached. Write a direct variation equation relating the weight x and the amount of stretch y.

• y = 0.5x

• y= 2x

• y= 5x + 10

• y= 2x +5