Question
If y is proportional to x, find the constant of proportionality.
2
4
6
8
2
4
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8
Answers
Answered by
GPT-4o mini
If \( y \) is proportional to \( x \), it can be expressed mathematically as:
\[
y = kx
\]
where \( k \) is the constant of proportionality.
From your message, it seems you've provided a list of numbers: 2, 4, 6, and 8. If we want to establish a relationship involving \( x \) and \( y \), we need to clarify the values of \( x \) corresponding to these \( y \)-values.
For example, if we take the first \( y \)-value (2) with its corresponding \( x \)-value (let's assume \( x=1 \)), we can calculate \( k \):
1. For \( y = 2 \) when \( x = 1 \):
\[
2 = k(1) \Rightarrow k = 2
\]
2. For \( y = 4 \) when \( x = 2 \):
\[
4 = k(2) \Rightarrow k = 2
\]
3. For \( y = 6 \) when \( x = 3 \):
\[
6 = k(3) \Rightarrow k = 2
\]
4. For \( y = 8 \) when \( x = 4 \):
\[
8 = k(4) \Rightarrow k = 2
\]
In each case, the constant of proportionality \( k \) equals \( 2 \).
Thus, if \( y \) is proportional to \( x \) and you have the values \( 2, 4, 6, 8 \) with the corresponding \( x \) values being \( 1, 2, 3, 4 \), the constant of proportionality is \( k = 2 \).
\[
y = kx
\]
where \( k \) is the constant of proportionality.
From your message, it seems you've provided a list of numbers: 2, 4, 6, and 8. If we want to establish a relationship involving \( x \) and \( y \), we need to clarify the values of \( x \) corresponding to these \( y \)-values.
For example, if we take the first \( y \)-value (2) with its corresponding \( x \)-value (let's assume \( x=1 \)), we can calculate \( k \):
1. For \( y = 2 \) when \( x = 1 \):
\[
2 = k(1) \Rightarrow k = 2
\]
2. For \( y = 4 \) when \( x = 2 \):
\[
4 = k(2) \Rightarrow k = 2
\]
3. For \( y = 6 \) when \( x = 3 \):
\[
6 = k(3) \Rightarrow k = 2
\]
4. For \( y = 8 \) when \( x = 4 \):
\[
8 = k(4) \Rightarrow k = 2
\]
In each case, the constant of proportionality \( k \) equals \( 2 \).
Thus, if \( y \) is proportional to \( x \) and you have the values \( 2, 4, 6, 8 \) with the corresponding \( x \) values being \( 1, 2, 3, 4 \), the constant of proportionality is \( k = 2 \).