To determine the constant of proportionality in the given equation [tex]\( y = 5x \)[/tex], let's break down the concept of a direct proportional relationship.
1. Understanding Direct Proportionality:
An equation represents a direct proportional relationship if it can be written in the form:
[tex]\[
y = kx
\][/tex]
where [tex]\( k \)[/tex] is the constant of proportionality. This [tex]\( k \)[/tex] represents how much [tex]\( y \)[/tex] changes for a given change in [tex]\( x \)[/tex].
2. Identify the Constant:
In the equation [tex]\( y = 5x \)[/tex], compare this with the standard form [tex]\( y = kx \)[/tex]. We can see that [tex]\( k = 5 \)[/tex].
3. Conclusion:
The coefficient of [tex]\( x \)[/tex] in the equation [tex]\( y = 5x \)[/tex] gives us the constant of proportionality, which is exactly 5.
Thus, the constant of proportionality in the equation [tex]\( y = 5x \)[/tex] is:
[tex]\[
\boxed{5}
\][/tex]
