To determine if the equation \( x = 9y \) represents a direct proportion and to identify the constant of proportionality, we should first isolate the variable \( y \).
1. Start with the given equation:
[tex]\[
x = 9y
\][/tex]
2. To isolate \( y \), divide both sides of the equation by 9:
[tex]\[
\frac{x}{9} = \frac{9y}{9}
\][/tex]
3. Simplify the right side:
[tex]\[
\frac{x}{9} = y
\][/tex]
4. Rearrange the equation to show \( y \) explicitly in terms of \( x \):
[tex]\[
y = \frac{x}{9}
\][/tex]
The equation \( y = \frac{x}{9} \) indeed represents a direct proportion, as \( y \) is directly proportional to \( x \).
The constant of proportionality is the factor by which \( x \) is multiplied to obtain \( y \). In this case, \( y = \frac{1}{9} x \), so the constant of proportionality is:
[tex]\[
\frac{1}{9} \approx 0.1111111111111111
\][/tex]
Therefore, the correct answer is:
Yes, [tex]\(\frac{1}{9}\)[/tex]
