Question

what is the constant of proportionality indicated in the table below?
x | 10 | 20 | 30 | 40
y | 2 | 4 | 6 | 8

Explanation:

Step1: Recall the formula for constant of proportionality

For two proportional quantities \( x \) and \( y \), the constant of proportionality \( k \) is given by \( k=\frac{x}{y} \) (if \( x \) is directly proportional to \( y \)).

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

Take \( x = 10 \) and \( y = 2 \). Then \( k=\frac{x}{y}=\frac{10}{2}=5 \).

Step3: Verify with other pairs

• For \( x = 20 \) and \( y = 4 \): \( \frac{20}{4}=5 \).
• For \( x = 30 \) and \( y = 6 \): \( \frac{30}{6}=5 \).
• For \( x = 40 \) and \( y = 8 \): \( \frac{40}{8}=5 \).

All pairs give the same value of \( k \).

Answer:

The constant of proportionality[LLM SSE On Failure]