To solve this problem, we first need to understand the concept of direct variation. When two variables [tex]\( x \)[/tex] and [tex]\( y \)[/tex] vary directly, they are related by the equation:
[tex]\[ x = ky \][/tex]
where [tex]\( k \)[/tex] is a constant.
### Step-by-Step Solution:
1. Identify the given values:
- When [tex]\( y = 3 \)[/tex], [tex]\( x = 10 \)[/tex].
2. Determine the constant of variation, [tex]\( k \)[/tex]:
Using the relationship [tex]\( x = ky \)[/tex], we can find [tex]\( k \)[/tex] as follows:
[tex]\[ k = \frac{x}{y} \][/tex]
Substituting the given values:
[tex]\[ k = \frac{10}{3} \][/tex]
[tex]\[ k = 3.3333333333333335 \][/tex]
3. Use the constant [tex]\( k \)[/tex] to find the new value of [tex]\( x \)[/tex] when [tex]\( y = 9 \)[/tex]:
Since [tex]\( x = ky \)[/tex],
[tex]\[ x = 3.3333333333333335 \times 9 \][/tex]
[tex]\[ x = 30.0 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 9 \)[/tex] is [tex]\( 30 \)[/tex].
So,
[tex]\[ x = 30 \][/tex]
