Question

Rooter Plus charges a $25 service fee plus $40 per hour of work done. Is this a proportional or non-proportional relationship?

Proportional; the constant of proportionality is $25/hour
Proportional; the constant of proportionality is $40/hour
Non-proportional; the rate of change is $25/hour
Non-proportional; the rate of change is $40/hour

Answer 1

Non-proportional; the rate of change is $40/hour

Explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form
`y/x=k` 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

Let

x -----> the number of hours

y ----> The total charge in dollars

The equation of the line in slope intercept form is equal to

`y=mx+b`

where

m is the slope

b is the y-intercept

we have

`m=40\ \$/h\\b=\$25`

substitute

`y=40x+25`

This relationship is not proportional, because the line not passes through the origin

therefore

Non-proportional; the rate of change is $40/hour