Slope Direct Variation Constant of Variation and Proportions

The constant value (often written k) relating amounts that rise or fall uniformly together.

• rate

• constant of proportionality

• direct variaton

• slope

Shows the relative sizes of two or more values.

3:1

3 to 1

3/1

• slope

• ratio

• direct variation

• proportion

In the graph below, y is directly proportional to x.

Based on the relationship shown in the graph, what is the value of y when x = 10?

• 45

• 40

• 35

• 30

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

• 26

• 3

• 58.5

• 2

The constant of variation is the same as the slope of the line.

• True

• Falsa

The graph of a direct variation relationship is shown. Based on the relationship shown in the graph, what is the value of y when x = 17?

• 12

• 68

• 94

• 8

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.

• 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.

• 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.

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