Certainly! Let’s find the constant of proportionality in the equation [tex]\(\frac{x}{y} = \frac{2}{9}\)[/tex].
An equation of the form [tex]\(\frac{x}{y} = \frac{2}{9}\)[/tex] represents a proportional relationship between [tex]\(x\)[/tex] and [tex]\(y\)[/tex]. In a proportional relationship, the ratio between two variables is constant.
To determine this constant of proportionality, observe the right-hand side of the equation, which is [tex]\(\frac{2}{9}\)[/tex].
Thus, the constant of proportionality in the equation [tex]\(\frac{x}{y} = \frac{2}{9}\)[/tex] is [tex]\(\frac{2}{9}\)[/tex].
The question provides multiple choices for the constant of proportionality:
- [tex]\(\frac{2}{9}\)[/tex]
- 2
- [tex]\(\frac{9}{2}\)[/tex]
- 9
Comparing these options to our derived constant of proportionality [tex]\(\frac{2}{9}\)[/tex], the correct answer is:
[tex]\[
\frac{2}{9}
\][/tex]
