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The value of [tex]$y$[/tex] varies directly with [tex]$x$[/tex]. If [tex][tex]$y = 3$[/tex][/tex] when [tex]$x = -1$[/tex], solve for [tex]k[/tex].

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

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

Sagot :

GinnyAnsweridn
To solve for the constant of variation [tex]\( k \)[/tex] in the equation where [tex]\( y \)[/tex] varies directly with [tex]\( x \)[/tex], we start with the given relationship:

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

Given:
[tex]\[ y = 3 \][/tex]
[tex]\[ x = -1 \][/tex]

We can substitute these values into the equation to solve for [tex]\( k \)[/tex]:

[tex]\[ 3 = k \cdot (-1) \][/tex]

Next, isolate [tex]\( k \)[/tex] by dividing both sides of the equation by [tex]\(-1\)[/tex]:

[tex]\[ k = \frac{3}{-1} \][/tex]

Simplifying this division:

[tex]\[ k = -3.0 \][/tex]

Thus, the value of [tex]\( k \)[/tex] is:

[tex]\[ k = -3.0 \][/tex]
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