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The value of [tex]$y$[/tex] varies directly with [tex]$x$[/tex]. If [tex][tex]$y = 40$[/tex][/tex] and [tex]$x = 8$[/tex], solve for [tex]k[/tex].

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

[tex]k = \, \text{[?]}[/tex]

Sagot :

GinnyAnswer
To solve for the constant [tex]\( k \)[/tex] in the direct variation equation [tex]\( y = kx \)[/tex], we follow these steps:

1. Identify the given values: We are provided with [tex]\( y = 40 \)[/tex] and [tex]\( x = 8 \)[/tex].

2. Write the direct variation equation: The relationship between [tex]\( y \)[/tex] and [tex]\( x \)[/tex] is given by [tex]\( y = kx \)[/tex]. We need to solve for [tex]\( k \)[/tex].

3. Substitute the given values into the equation:
[tex]\[ 40 = k \cdot 8 \][/tex]

4. Solve for [tex]\( k \)[/tex]:
[tex]\[ k = \frac{40}{8} \][/tex]

5. Calculate the value:
[tex]\[ k = 5.0 \][/tex]

Thus, the constant [tex]\( k \)[/tex] is [tex]\( 5.0 \)[/tex].
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