Respuesta :

we know that

A relationship between two variables, x, and y, represent a direct variation if it can be expressed in the form [tex]\frac{y}{x}=k[/tex] or [tex]y=kx[/tex]

where

k is the constant of proportionality

In this problem we have

[tex]y=2.5x[/tex]

so

the constant of proportionality k is equal to

[tex]k=2.5[/tex]

therefore

the answer is

[tex]k=2.5[/tex]

The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]

Further explanation:

The relation is defined as the relationship between the input values and output values.

The x coordinates are the domain of the function and the y coordinates are the range of the function.

Given:

The equation is [tex]y = 2.5x.[/tex]

Explanation:

The proportionality equation can be expressed as follows,

[tex]y \propto x[/tex]

The value of [tex]y[/tex] changes as [tex]x[/tex] changes. If the value of [tex]x[/tex] increases then the value of y is also increasing.

The equation can be expressed as follows,

[tex]y = kx[/tex]

The inversely proportional relationship can be expressed as,

[tex]y \propto \dfrac{1}{x}[/tex]

Here, [tex]k[/tex] is the proportionality constant.

The given equation is [tex]y = 2.5x.[/tex]

The y is the independent variable and [tex]x[/tex] is the dependent variable.

The proportionality constant is 2.5.

The constant of proportionality in the equation [tex]y = 2.5x[/tex] is [tex]\boxed{2.5}.[/tex]

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function https://brainly.com/question/3412497

Answer details:

Grade: High School

Subject: Mathematics

Chapter: Ratio and proportion

Keywords: proportional, directly proportional, constant, proportionality equation, y=0.41x, constant of proportionality.