Question

Question content area left
Part 1
Error Analysis  The table shows a proportional relationship between x and y. Katerina has to complete the table. Katerina incorrectly says the ratio StartFraction y Over x EndFraction
is one tenth
. Complete the table. What error did Katerina likely​ make?
x
y
Ratio StartFraction y Over x EndFraction
3
30
​?
5
50
​?
7
70
​?
.
.
.
Question content area right
Part 1
Complete the table.
x
y
Ratio StartFraction y Over x EndFraction
3
30
  
enter your response here
5
50
  
enter your response here
7
70
  
enter your response here
​(Simplify your​ answers.)

Answer 1

To complete the table and analyze the error made by Katerina, let's first evaluate the proportional relationship between \( x \) and \( y \).

Given the values in the table:
- When \( x = 3 \), \( y = 30 \)
- When \( x = 5 \), \( y = 50 \)
- When \( x = 7 \), \( y = 70 \)

We can calculate the ratio \( \frac{y}{x} \) for each pair:

1. For \( x = 3 \):
\[
\frac{y}{x} = \frac{30}{3} = 10
\]

2. For \( x = 5 \):
\[
\frac{y}{x} = \frac{50}{5} = 10
\]

3. For \( x = 7 \):
\[
\frac{y}{x} = \frac{70}{7} = 10
\]

This indicates that the ratio \( \frac{y}{x} \) is consistently 10 for the values provided, not \( \frac{1}{10} \) as Katerina erroneously stated.

Now, we can fill in the table with the simplified ratios:

| \( x \) | \( y \) | Ratio \( \frac{y}{x} \) |
|---------|---------|---------------------------|
| 3 | 30 | 10 |
| 5 | 50 | 10 |
| 7 | 70 | 10 |

### Likely Error
The error Katerina likely made was misunderstanding the proportional relationship and possibly miscalculating the division or misinterpreting the terms of the ratio. She stated the ratio as \( \frac{1}{10} \), which indicates a misunderstanding of how \( y \) is related to \( x \). The correct ratio demonstrates that \( y \) is actually 10 times \( x \), rather than \( x \) being one-tenth of \( y \).