Question

Why does.the equation y=3x+5 NOT represent a proportional relationship

Answer 1

Answer:

The equation not represent a proportional relationship because the line don't passes through the origin

Step-by-step explanation:

we know that

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

In a proportional relationship the constant of proportionality k is equal to the slope m of the line and the line passes through the origin

so

In this problem we have

$y=3x+5$

This is the equation of the line in slope intercept form

where

the slope is m=5

the y-intercept is b=5

Remember that in a proportional relationship the value of b must be equal to zero (because the line passes through the origin)

therefore

The equation not represent a proportional relationship because the line don't passes through the origin