Certainly! Let's solve this step-by-step.
1. Understand the concept of direct variation:
When we say that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], it means there exists a constant [tex]\( k \)[/tex] such that:
[tex]\[
y = kx
\][/tex]
2. Identify the given points:
We are provided with the values [tex]\( y = 72 \)[/tex] when [tex]\( x = 9 \)[/tex]. Using this information, we can find the constant of variation [tex]\( k \)[/tex].
3. Find the constant of variation [tex]\( k \)[/tex]:
Substitute [tex]\( x = 9 \)[/tex] and [tex]\( y = 72 \)[/tex] into the direct variation equation:
[tex]\[
72 = k \cdot 9
\][/tex]
To solve for [tex]\( k \)[/tex], divide both sides by 9:
[tex]\[
k = \frac{72}{9} = 8
\][/tex]
4. Use the constant [tex]\( k \)[/tex] to find [tex]\( y \)[/tex] when [tex]\( x = 17 \)[/tex]:
Now that we have [tex]\( k = 8 \)[/tex], we can use this in the direct variation equation to find [tex]\( y \)[/tex] when [tex]\( x = 17 \)[/tex]:
[tex]\[
y = kx = 8 \times 17
\][/tex]
5. Calculate the value of [tex]\( y \)[/tex]:
[tex]\[
y = 8 \times 17 = 136
\][/tex]
So, when [tex]\( x = 17 \)[/tex], [tex]\( y \)[/tex] is:
[tex]\[
y = 136
\][/tex]
Therefore, [tex]\( y \)[/tex] equals 136 when [tex]\( x \)[/tex] is 17.
