Question

Question

Use the table to answer the question.

Time (hours) Pages read
12 15
1 30
112 45
2 60
Ruth can read 15 pages in 30 minutes. She decides to create a table to keep track of her progress. From the data provided, at what ratio is the constant of proportionality?

(1 point)
Responses

(112, 30)
left parenthesis 1 Start Fraction 1 over 2 End Fraction comma 30 right parenthesis

(1, 30)
left parenthesis 1 comma 30 right parenthesis

(15, 12)
left parenthesis 15 comma Start Fraction 1 over 2 End Fraction right parenthesis

(2, 60)

Answer 1

To find the constant of proportionality from the data, we can calculate the ratio of pages read to time taken.

The constant of proportionality \( k \) can be calculated as:

\[ k = \frac{\text{Pages read}}{\text{Time (hours)}}. \]

Let's calculate \( k \) for each entry in the table:

1. For \( (12, 15) \): \[ k = \frac{15}{12} = 1.25. \]

2. For \( (1, 30) \): \[ k = \frac{30}{1} = 30. \]

3. For \( (112, 45) \): \[ k = \frac{45}{112} \approx 0.4018. \]

4. For \( (2, 60) \): \[ k = \frac{60}{2} = 30. \]

From this analysis, we can see that the consistent values of \( k \) are \( 30 \) for the entries \( (1, 30) \) and \( (2, 60) \).

Thus, the entry that shows a consistent ratio and thus represents the constant of proportionality is \( (1, 30) \).

So, the answer is:

(1, 30).