To solve the problem where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we start by using the concept of direct variation. Direct variation can be modeled with the equation:
[tex]\[ y = kx \][/tex]
where [tex]\( k \)[/tex] is the constant of variation.
### Step 1: Determine the Constant of Variation
First, we need to find the constant [tex]\( k \)[/tex] using the given values [tex]\( y = 14 \)[/tex] and [tex]\( x = 2 \)[/tex].
[tex]\[ 14 = k \cdot 2 \][/tex]
To solve for [tex]\( k \)[/tex], we divide both sides of the equation by 2:
[tex]\[ k = \frac{14}{2} = 7 \][/tex]
So, the constant of variation [tex]\( k \)[/tex] is 7.
### Step 2: Use the Constant to Find the Unknown Value
Now that we have [tex]\( k = 7 \)[/tex], we can use it to find the value of [tex]\( x \)[/tex] when [tex]\( y = 35 \)[/tex].
Using the direct variation formula [tex]\( y = kx \)[/tex]:
[tex]\[ 35 = 7x \][/tex]
To find [tex]\( x \)[/tex], we divide both sides by 7:
[tex]\[ x = \frac{35}{7} = 5 \][/tex]
Therefore, the value of [tex]\( x \)[/tex] when [tex]\( y = 35 \)[/tex] is:
[tex]\[ x = 5 \][/tex]
