Sophia earns $12 per hour working in an office plus $5 dollars for parking fees. She uses the function e = 12h + 5 to represents her daily earnings, where e represents her earnings and h represents the number of hours she works. Explain whether or not the function has a proportional relationship.

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

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

In this problem we have

[tex]e=12h+5[/tex]

This is the equation of the line in slope intercept form

where

e ---> represents her daily earnings

h ---> represents the number of hours she works

we have

The slope is equal to [tex]m=\$12\ per\ hour[/tex]

The y-intercept is [tex]b=\$5[/tex]

Remember that

In a proportional relationship the y-intercept is equal to zero, because the line passes through the origin

In this problem, the y-intercept is not equal to zero, so this line don't pass through the origin

therefore

The given function is not a proportional relationship