Answer:
n = 7m
Step-by-step explanation:
The general equation of a direct proportional relationship is:
[tex]\boxed{\begin{array}{l}\underline{\textsf{Direct Proportionality Equation}}\\\\y=kx\\\\\textsf{where:}\\\phantom{ww}\bullet\;\;\textsf{$x$ is the independent variable.}\\\phantom{ww}\bullet\;\;\textsf{$y$ is the dependent variable.}\\\phantom{ww}\bullet\;\;\textsf{$k$ is the constant of proportionality.}\end{array}}[/tex]
In a proportional relationship, the ratio between y and x is constant.
In this case, m is the independent variable and n is the dependent variable. Therefore:
[tex]n = km[/tex]
To determine the equation that describes the proportional relationship between m and n, we need to identify the constant of proportionality (k).
Rearrange the equation to isolate k:
[tex]k=\dfrac{n}{m}[/tex]
Now, substitute the values from the table into the equation:
For m = 3 and n = 21:
[tex]k=\dfrac{n}{m} = \dfrac{21}{3} = 7[/tex]
For m = 5 and n = 35:
[tex]k=\dfrac{n}{m} = \dfrac{35}{5} = 7[/tex]
For m = 8 and n = 56:
[tex]k=\dfrac{n}{m} = \dfrac{56}{8} = 7[/tex]
Since the ratio n/m is constant and equal to 7, the relationship between m and n can be expressed by the equation:
[tex]\LARGE\boxed{\boxed{n = 7m}}[/tex]