Answer:
Yes, y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship and the constant of proportionality is [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
The Proportional is a relationship between two quantity one of them equals the product of the other and a constant, where this constant called the constant of proportionality
Let us solve the question
∵ y = [tex]\frac{1}{5}[/tex] x
→ It the same as the form of the proportional equation above
∵ [tex]\frac{1}{5}[/tex] is a constant
∴ y is the product of x and constant
∴ y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship
Substitute x by 0 to find y and show it represented by a line passing through the origin
∵ x = 0
∴ y = [tex]\frac{1}{5}[/tex] (0) = 0
→ That means point (0, 0) lies on the line which represents the equation
∴ The line which represents this relation is passing through the origin
∴ y = [tex]\frac{1}{5}[/tex] x represents a proportional relationship
∵ y = kx, k is the constant of proportionality
∵ y = [tex]\frac{1}{5}[/tex] x
∴ k = [tex]\frac{1}{5}[/tex]
∴ The constant of proportionality is [tex]\frac{1}{5}[/tex]
