Question

Drag the proportional relationships to order the unit rates from LEAST to GREATEST

Answer 1

To be able to order the unit rate of the proportional relationships from least to greatest, the first step is to determine the value of the unit rate of each relationship.

Relationship A

To determine the unit rate of the relationship, you have to choose two points of the graph and calculate the slope of the line using the formula:

`m=(y_2-y_1)/(x_2-x_1)`

Use for example the points (4,10) and (0,0)

`\begin{gathered} m=(10-0)/(4-0) \\ m=(10)/(4) \\ m=2.5 \end{gathered}`

Relationship B

Using the same formula as before, you can determine the unit rate of the relationship shown on the table.

Choose two points, for example, the points (9,23.4) and (6,15.6)

`\begin{gathered} m=(23.4-15.6)/(9-6) \\ m=(7.8)/(3) \\ m=2.6 \end{gathered}`

Relationship C

This relationship is presented as a linear equation, the unit rate of the relationship is equal to the coefficient of the x-term:

`y=2.51x`

The unit rate of the relationship is m=2.51

The unit rates of the 3 relationships are:

A- 2.5

B- 2.6

C- 2.51

Ordered from least to greatest are:

Relationship A → Relationship C → Relationship B