Question
What is the constant of proportionality in this proportional relationship?
x 2 3 4 5
y 159 239 319 389
Responses
79
7 over 9
97
9 over 7
7
7
9
9
x 2 3 4 5
y 159 239 319 389
Responses
79
7 over 9
97
9 over 7
7
7
9
9
Answers
GPT-4o mini
To find the constant of proportionality in a proportional relationship, we can divide the value of \( y \) by the corresponding value of \( x \). The constant of proportionality \( k \) can be expressed as:
\[
k = \frac{y}{x}
\]
Let's calculate \( k \) for a few pairs of \( (x, y) \):
1. For \( x = 2, y = 159 \):
\[
k = \frac{159}{2} = 79.5
\]
2. For \( x = 3, y = 239 \):
\[
k = \frac{239}{3} = 79.67
\]
3. For \( x = 4, y = 319 \):
\[
k = \frac{319}{4} = 79.75
\]
4. For \( x = 5, y = 389 \):
\[
k = \frac{389}{5} = 77.8
\]
As we see from the calculations, \( k \) is not constant throughout the values given. This indicates that the relationship is not perfectly proportional. Since the options do not correspond to a consistent mathematical constant based on these calculations, it appears that either the relationship is truly not proportional or we need further context or a different interpretation to align with the provided choices.
However, there seems to be no clear answer based on straightforward calculations, therefore we can assert that none of the listed options \( 79, \frac{7}{9}, 97, \frac{9}{7}, 7, 9 \) accurately fits the description of a consistent constant of proportionality given the calculated values for \( k \).
\[
k = \frac{y}{x}
\]
Let's calculate \( k \) for a few pairs of \( (x, y) \):
1. For \( x = 2, y = 159 \):
\[
k = \frac{159}{2} = 79.5
\]
2. For \( x = 3, y = 239 \):
\[
k = \frac{239}{3} = 79.67
\]
3. For \( x = 4, y = 319 \):
\[
k = \frac{319}{4} = 79.75
\]
4. For \( x = 5, y = 389 \):
\[
k = \frac{389}{5} = 77.8
\]
As we see from the calculations, \( k \) is not constant throughout the values given. This indicates that the relationship is not perfectly proportional. Since the options do not correspond to a consistent mathematical constant based on these calculations, it appears that either the relationship is truly not proportional or we need further context or a different interpretation to align with the provided choices.
However, there seems to be no clear answer based on straightforward calculations, therefore we can assert that none of the listed options \( 79, \frac{7}{9}, 97, \frac{9}{7}, 7, 9 \) accurately fits the description of a consistent constant of proportionality given the calculated values for \( k \).