Question

ted joined a book club. this table shows the proportional relationship bet ted has spent reading a book, and y, the number of pages he has read.
x (hours) | y (pages)
1 | 23
2 | 46
3 | 69
4 | 92
what is the constant of proportionality? write your answer as a whole num
□ pages per hour

Explanation:

Step1: Recall the formula for constant of proportionality

For a proportional relationship \( y = kx \), the constant of proportionality \( k \) is given by \( k=\frac{y}{x} \).

Step2: Calculate \( k \) using the first pair of values

Using \( x = 1 \) and \( y = 23 \), we substitute into the formula: \( k=\frac{23}{1}=23 \).

Step3: Verify with other pairs (optional but good practice)

• For \( x = 2 \), \( y = 46 \): \( k=\frac{46}{2}=23 \).
• For \( x = 3 \), \( y = 69 \): \( k=\frac{69}{3}=23 \).
• For \( x = 4 \), \( y = 92 \): \( k=\frac{92}{4}=23 \).

All pairs give \( k = 23 \), so the constant of proportionality is 23.

Answer:

23