[tex] y [/tex] varies directly with [tex] x [/tex]. [tex] y [/tex] is 72 when [tex] x [/tex] is 9. What is [tex] y [/tex] when [tex] x [/tex] is 17?

[tex] y = [?] [/tex]



Answer :

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.