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Sagot :
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]
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]
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