To determine the constant of proportionality from the data table provided, we need to find the ratio of pages read to time in hours for each entry.
The ratio can be calculated as follows:
- For \( \frac{1}{2} \) hours (30 minutes), Ruth reads 15 pages. So the ratio is \( \frac{15}{\frac{1}{2}} = 15 \times 2 = 30 \).
- For 1 hour, she reads 30 pages. The ratio is \( \frac{30}{1} = 30 \).
- For \( \frac{3}{2} \) hours (90 minutes), she reads 45 pages. The ratio is \( \frac{45}{\frac{3}{2}} = 45 \times \frac{2}{3} = 30 \).
- For 2 hours, she reads 60 pages. The ratio is \( \frac{60}{2} = 30 \).
In every case, the constant of proportionality is 30 pages per hour.
Now, looking at the given responses, the appropriate answer that reflects a time of 1 hour and 30 pages read is:
(1, 30), left parenthesis 1 comma 30 right parenthesis.
This indicates a ratio of 30 pages per hour, confirming our calculations.