Question

the equation y = 1/5x represents a proportional relationship. explain how you can tell the relationship is proportional from the graph of the equation, and you can find the constan of proportionality.

Answer 1

Yes, y =
`(1)/(5)` x represents a proportional relationship and the constant of proportionality is
`(1)/(5)`

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

• If x and y are proportion, then y = k x, where k is the constant of proportionality

• The proportional relationship represented graphically by a line passing through the origin point (0, 0)

Let us solve the question

∵ y =
`(1)/(5)` x

→ It the same as the form of the proportional equation above

∵
`(1)/(5)` is a constant

∴ y is the product of x and constant

∴ y =
`(1)/(5)` 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 =
`(1)/(5)` (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 =
`(1)/(5)` x represents a proportional relationship

∵ y = kx, k is the constant of proportionality

∵ y =
`(1)/(5)` x

∴ k =
`(1)/(5)`

∴ The constant of proportionality is
`(1)/(5)`