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].
