Question

1.
Find the constant of variation k for the direct variation.

x f ( x )
0 0
3 6
4 8
7 14

Answer 1

In a direct variation, the relationship between \( x \) and \( f(x) \) can be expressed as:

\[
f(x) = kx
\]

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

To find \( k \), we can use the provided pairs \((x, f(x))\) where \( f(x) \) is not zero:

1. For the pair \( (3, 6) \):
\[
6 = k \cdot 3 \implies k = \frac{6}{3} = 2
\]

2. For the pair \( (4, 8) \):
\[
8 = k \cdot 4 \implies k = \frac{8}{4} = 2
\]

3. For the pair \( (7, 14) \):
\[
14 = k \cdot 7 \implies k = \frac{14}{7} = 2
\]

In all cases, we find that:

\[
k = 2
\]

Thus, the constant of variation \( k \) is \( 2 \).