Question
or
During the summer, Dwayne works on his uncle's dairy farm. One of Dwayne's many chores is to load bales of hay onto a wagon and haul them from the field into the barn.
There is a proportional relationship between the number of wagon loads, x, and the number of bales of hay Dwayne can haul, y.
x (wagon loads) y (bales)
1 4
2 8
4 16
5 20
What is the constant of proportionality? Write your answer as a whole number or decimal.
bales per wagon load
Answers
Answered by
GPT-4o mini
To find the constant of proportionality in the relationship between the number of wagon loads (x) and the bales of hay (y), we can use the formula:
\[
k = \frac{y}{x}
\]
where \( k \) is the constant of proportionality.
We can calculate \( k \) using any of the pairs from the table you provided. Let's use the first pair (1 wagon load and 4 bales):
\[
k = \frac{y}{x} = \frac{4}{1} = 4
\]
To verify, we can calculate \( k \) using the other pairs:
- For \( x = 2 \), \( y = 8 \):
\[
k = \frac{8}{2} = 4
\]
- For \( x = 4 \), \( y = 16 \):
\[
k = \frac{16}{4} = 4
\]
- For \( x = 5 \), \( y = 20 \):
\[
k = \frac{20}{5} = 4
\]
In all cases, the constant of proportionality \( k \) is consistently 4.
Thus, the constant of proportionality is \( 4 \) bales per wagon load.
\[
k = \frac{y}{x}
\]
where \( k \) is the constant of proportionality.
We can calculate \( k \) using any of the pairs from the table you provided. Let's use the first pair (1 wagon load and 4 bales):
\[
k = \frac{y}{x} = \frac{4}{1} = 4
\]
To verify, we can calculate \( k \) using the other pairs:
- For \( x = 2 \), \( y = 8 \):
\[
k = \frac{8}{2} = 4
\]
- For \( x = 4 \), \( y = 16 \):
\[
k = \frac{16}{4} = 4
\]
- For \( x = 5 \), \( y = 20 \):
\[
k = \frac{20}{5} = 4
\]
In all cases, the constant of proportionality \( k \) is consistently 4.
Thus, the constant of proportionality is \( 4 \) bales per wagon load.