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The value of [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex]. If [tex]\( y = -51 \)[/tex] and [tex]\( x = 3 \)[/tex], solve for [tex]\( k \)[/tex].

Remember: [tex]\( y = k x \)[/tex]

[tex]\[ k = [?] \][/tex]

Sagot :

GinnyAnswer
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]
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