To find the constant of proportionality in the equation [tex]\(\frac{x}{y} = \frac{2}{g}\)[/tex], let's analyze and solve it step-by-step:
1. Understand the equation:
[tex]\[\frac{x}{y} = \frac{2}{g}\][/tex]
This equation indicates that [tex]\(x\)[/tex] is directly proportional to [tex]\(y\)[/tex], with [tex]\(\frac{2}{g}\)[/tex] being the constant of proportionality.
2. Rewrite the equation:
To make it clearer, let's isolate [tex]\(x\)[/tex] on one side of the equation:
[tex]\[x = \left(\frac{2}{g}\right) y\][/tex]
By doing this, it becomes evident that [tex]\(\frac{2}{g}\)[/tex] is the factor that relates [tex]\(x\)[/tex] to [tex]\(y\)[/tex].
3. Identify the constant of proportionality:
The constant of proportionality in this equation is the multiplicative factor that relates [tex]\(x\)[/tex] and [tex]\(y\)[/tex], which is [tex]\(\frac{2}{g}\)[/tex].
4. Consider the possible values:
We are given the following choices for the constant of proportionality:
[tex]\[\frac{2}{9}, \quad 2, \quad \frac{9}{2}, \quad 9\][/tex]
5. Determine the correct value:
The best choice that fits in the context of our equation [tex]\(\frac{x}{y} = \frac{2}{g}\)[/tex] is [tex]\(2\)[/tex]. This is because the numerical value for the constant of proportionality simplifies to [tex]\(2\)[/tex] when the correct proportional relationship aligns perfectly with [tex]\(\frac{2}{g}\)[/tex].
Therefore, the constant of proportionality is:
[tex]\[ \boxed{2} \][/tex]
