Question
Do the two tables show the same proportional relationship between x and y? Explain.
x
50
75
100
y
1,250
1,875
2,500
x
3
4
5
y
4.2
5.6
7
Question content area bottom
Part 1
▼
No,
Yes,
each table shows
▼
the same
a different
proportional relationship. In the first table, every ratio StartFraction y Over x EndFraction
is equivalent to
enter your response here. In the second table, every ratio StartFraction y Over x EndFraction
is equivalent to
enter your response here.
(Simplify your answers.)
x
50
75
100
y
1,250
1,875
2,500
x
3
4
5
y
4.2
5.6
7
Question content area bottom
Part 1
▼
No,
Yes,
each table shows
▼
the same
a different
proportional relationship. In the first table, every ratio StartFraction y Over x EndFraction
is equivalent to
enter your response here. In the second table, every ratio StartFraction y Over x EndFraction
is equivalent to
enter your response here.
(Simplify your answers.)
Answers
GPT-4o mini
To determine whether the two tables show the same proportional relationship between \( x \) and \( y \), we need to calculate the ratio \( \frac{y}{x} \) for each pair in both tables and see if they remain constant.
### For the first table:
| \( x \) | \( y \) |
|---------|---------|
| 50 | 1250 |
| 75 | 1875 |
| 100 | 2500 |
Calculating the ratios:
1. For the first pair:
\[
\frac{y}{x} = \frac{1250}{50} = 25
\]
2. For the second pair:
\[
\frac{y}{x} = \frac{1875}{75} = 25
\]
3. For the third pair:
\[
\frac{y}{x} = \frac{2500}{100} = 25
\]
Each ratio \( \frac{y}{x} \) is equivalent to 25 in the first table.
### For the second table:
| \( x \) | \( y \) |
|---------|---------|
| 3 | 4.2 |
| 4 | 5.6 |
| 5 | 7 |
Calculating the ratios:
1. For the first pair:
\[
\frac{y}{x} = \frac{4.2}{3} \approx 1.4
\]
2. For the second pair:
\[
\frac{y}{x} = \frac{5.6}{4} = 1.4
\]
3. For the third pair:
\[
\frac{y}{x} = \frac{7}{5} = 1.4
\]
Each ratio \( \frac{y}{x} \) is equivalent to 1.4 in the second table.
### Conclusion:
The two tables do not show the same proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to **25**. In the second table, every ratio \( \frac{y}{x} \) is equivalent to **1.4**.
### Final answer:
No, each table shows a different proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to **25**. In the second table, every ratio \( \frac{y}{x} \) is equivalent to **1.4**.
### For the first table:
| \( x \) | \( y \) |
|---------|---------|
| 50 | 1250 |
| 75 | 1875 |
| 100 | 2500 |
Calculating the ratios:
1. For the first pair:
\[
\frac{y}{x} = \frac{1250}{50} = 25
\]
2. For the second pair:
\[
\frac{y}{x} = \frac{1875}{75} = 25
\]
3. For the third pair:
\[
\frac{y}{x} = \frac{2500}{100} = 25
\]
Each ratio \( \frac{y}{x} \) is equivalent to 25 in the first table.
### For the second table:
| \( x \) | \( y \) |
|---------|---------|
| 3 | 4.2 |
| 4 | 5.6 |
| 5 | 7 |
Calculating the ratios:
1. For the first pair:
\[
\frac{y}{x} = \frac{4.2}{3} \approx 1.4
\]
2. For the second pair:
\[
\frac{y}{x} = \frac{5.6}{4} = 1.4
\]
3. For the third pair:
\[
\frac{y}{x} = \frac{7}{5} = 1.4
\]
Each ratio \( \frac{y}{x} \) is equivalent to 1.4 in the second table.
### Conclusion:
The two tables do not show the same proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to **25**. In the second table, every ratio \( \frac{y}{x} \) is equivalent to **1.4**.
### Final answer:
No, each table shows a different proportional relationship. In the first table, every ratio \( \frac{y}{x} \) is equivalent to **25**. In the second table, every ratio \( \frac{y}{x} \) is equivalent to **1.4**.