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The value of [tex]$y$[/tex] varies directly with [tex]$x$[/tex]. If [tex]$y = -16$[/tex], then [tex][tex]$x = 4$[/tex][/tex]. Solve for [tex]$k$[/tex].

Remember: [tex]$y = kx$[/tex]

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

Sagot :

GinnyAnswer
Certainly! Let's solve for [tex]\( k \)[/tex] step by step.

1. Understand the relationship: The problem states that [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex]. This means we can use the direct variation formula:

[tex]\[ y = kx \][/tex]

2. Substitute the given values: We're given that [tex]\( y = -16 \)[/tex] and [tex]\( x = 4 \)[/tex]. Plug these values into the equation:

[tex]\[ -16 = k \times 4 \][/tex]

3. Solve for [tex]\( k \)[/tex]: Isolate [tex]\( k \)[/tex] by dividing both sides of the equation by 4:

[tex]\[ k = \frac{-16}{4} \][/tex]

4. Simplify the result:

[tex]\[ k = -4 \][/tex]

So, the constant of variation [tex]\( k \)[/tex] is [tex]\(-4\)[/tex].
Therefore,

[tex]\[ k = -4.0 \][/tex]
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