Question

If y is proportional to x, find the constant of proportionality.
x y
6 48
9 72

2
9
6
8

Answer 1

When \( y \) is said to be proportional to \( x \), it means that \( y = kx \) for some constant \( k \), known as the constant of proportionality.

We can find \( k \) using the pairs of \( x \) and \( y \) given.

Using the first pair \((x = 6, y = 48)\):

\[
y = kx \implies 48 = k \cdot 6
\]

To solve for \( k \):

\[
k = \frac{48}{6} = 8
\]

Using the second pair \((x = 9, y = 72)\):

\[
y = kx \implies 72 = k \cdot 9
\]

To solve for \( k \):

\[
k = \frac{72}{9} = 8
\]

In both cases, we find that the constant of proportionality \( k \) is \( 8 \).

Thus, the constant of proportionality is \( \boxed{8} \).