Answer :
To determine the constant of proportionality in the equation [tex]\( y = \frac{x}{9} \)[/tex], let’s analyze the given equation step by step.
1. Understand the Equation:
The equation is given as:
[tex]\[ y = \frac{x}{9} \][/tex]
2. Identify the Form of the Equation:
This can be rewritten in a more general form of [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
3. Rewrite the Given Equation:
Let's rewrite [tex]\( y = \frac{x}{9} \)[/tex] in the form [tex]\( y = kx \)[/tex]:
[tex]\[ y = \frac{1}{9} \cdot x \][/tex]
4. Determine the Constant [tex]\( k \)[/tex]:
By comparing [tex]\( y = \frac{1}{9} \cdot x \)[/tex] with [tex]\( y = kx \)[/tex], we can see that the constant [tex]\( k \)[/tex] is [tex]\( \frac{1}{9} \)[/tex].
Therefore, the constant of proportionality in the equation [tex]\( y = \frac{x}{9} \)[/tex] is:
[tex]\[ \frac{1}{9} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{\frac{1}{9}} \][/tex]
1. Understand the Equation:
The equation is given as:
[tex]\[ y = \frac{x}{9} \][/tex]
2. Identify the Form of the Equation:
This can be rewritten in a more general form of [tex]\( y = kx \)[/tex], where [tex]\( k \)[/tex] is the constant of proportionality.
3. Rewrite the Given Equation:
Let's rewrite [tex]\( y = \frac{x}{9} \)[/tex] in the form [tex]\( y = kx \)[/tex]:
[tex]\[ y = \frac{1}{9} \cdot x \][/tex]
4. Determine the Constant [tex]\( k \)[/tex]:
By comparing [tex]\( y = \frac{1}{9} \cdot x \)[/tex] with [tex]\( y = kx \)[/tex], we can see that the constant [tex]\( k \)[/tex] is [tex]\( \frac{1}{9} \)[/tex].
Therefore, the constant of proportionality in the equation [tex]\( y = \frac{x}{9} \)[/tex] is:
[tex]\[ \frac{1}{9} \][/tex]
Hence, the correct answer is:
[tex]\[ \boxed{\frac{1}{9}} \][/tex]
