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

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 or

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

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

f(x)=2/3x-8, which give g(x) the greatest value.

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.