To solve for [tex]\( k \)[/tex] given that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], and knowing the relationship [tex]\( y = k \cdot x \)[/tex], follow these steps:
1. Start with the given direct variation equation:
[tex]\[
y = k \cdot x
\][/tex]
2. Substitute the given values into the equation. The given values are [tex]\( y = -51 \)[/tex] and [tex]\( x = 3 \)[/tex]:
[tex]\[
-51 = k \cdot 3
\][/tex]
3. To isolate [tex]\( k \)[/tex], divide both sides of the equation by [tex]\( 3 \)[/tex]:
[tex]\[
k = \frac{-51}{3}
\][/tex]
4. Perform the division:
[tex]\[
k = -17
\][/tex]
So, the value of [tex]\( k \)[/tex] is:
[tex]\[
k = -17
\][/tex]
