Question
What is the constant of proportionality in this proportional relationship?
x 2 3 4 5
y 159 239 319 389
Responses
x 2 3 4 5
y 159 239 319 389
Responses
Answers
GPT-4o mini
To find the constant of proportionality in a proportional relationship, we need to determine if there is a constant ratio of \( y \) to \( x \) across all given pairs of values. The constant of proportionality (denoted as \( k \)) can be found using the equation:
\[
k = \frac{y}{x}
\]
Let's calculate \( k \) for each pair of \( (x, y) \):
1. For \( x = 2, y = 159 \):
\[
k = \frac{159}{2} = 79.5
\]
2. For \( x = 3, y = 239 \):
\[
k = \frac{239}{3} \approx 79.67
\]
3. For \( x = 4, y = 319 \):
\[
k = \frac{319}{4} = 79.75
\]
4. For \( x = 5, y = 389 \):
\[
k = \frac{389}{5} = 77.8
\]
Since the values of \( k \) are not constant, the relationship is not proportional. Therefore, there is no single constant of proportionality for the given data.
\[
k = \frac{y}{x}
\]
Let's calculate \( k \) for each pair of \( (x, y) \):
1. For \( x = 2, y = 159 \):
\[
k = \frac{159}{2} = 79.5
\]
2. For \( x = 3, y = 239 \):
\[
k = \frac{239}{3} \approx 79.67
\]
3. For \( x = 4, y = 319 \):
\[
k = \frac{319}{4} = 79.75
\]
4. For \( x = 5, y = 389 \):
\[
k = \frac{389}{5} = 77.8
\]
Since the values of \( k \) are not constant, the relationship is not proportional. Therefore, there is no single constant of proportionality for the given data.