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:
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Use for example the points (4,10) and (0,0)
[tex]\begin{gathered} m=\frac{10-0}{4-0} \\ m=\frac{10}{4} \\ m=2.5 \end{gathered}[/tex]
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)
[tex]\begin{gathered} m=\frac{23.4-15.6}{9-6} \\ m=\frac{7.8}{3} \\ m=2.6 \end{gathered}[/tex]
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:
[tex]y=2.51x[/tex]
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
