Question

If y is proportional to x, find the constant of proportionality.
x y
1 8
2 16
3 24
4 32

7
8
9
10

Answer 1

If \( y \) is proportional to \( x \), we can express this relationship mathematically as:

\[
y = kx
\]

where \( k \) is the constant of proportionality.

We can determine the constant \( k \) using any pair of values from the provided table. Let's take the first pair \((x, y) = (1, 8)\):

\[
8 = k \cdot 1 \implies k = 8
\]

We can verify this with the other pairs as well:

1. For \( x = 2 \):
\[
y = k \cdot 2 \implies 16 = k \cdot 2 \implies k = \frac{16}{2} = 8
\]

2. For \( x = 3 \):
\[
y = k \cdot 3 \implies 24 = k \cdot 3 \implies k = \frac{24}{3} = 8
\]

3. For \( x = 4 \):
\[
y = k \cdot 4 \implies 32 = k \cdot 4 \implies k = \frac{32}{4} = 8
\]

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

Thus, the constant of proportionality is:

\[
\boxed{8}
\]