Question

1. a food truck charges a constant rate per meal that can be represented by a proportional relationship. which equation could represent the relationship between the number of meals ordered, x, and the total cost, y? a. y = x + 8 b. y = 8x c. y = 4.50 + x d. y = 8x + 4.50 2. a mobile tech repair company charges a fee for the service call, plus a rate for each hour of work. the relationship can be represented with the equation y = 25.50x + 50. which statement best describes this scenario? a. proportional; the tech company charges a constant rate per hour. b. nonproportional; there is a fixed start amount. c. proportional; the service call does not change the total. d. nonproportional; the hourly rate changes over time.

Explanation:

Step1: Recall proportional - relationship formula

A proportional relationship has the form $y = kx$, where $k$ is the constant of proportionality and there is no added constant term.

Step2: Analyze food - truck problem

For the food - truck charging a constant rate per meal (proportional relationship), the equation should be of the form $y=kx$. Among the options $y = x + 8$, $y=4.50 + x$, $y = 8x+4.50$, and $y = 8x$, the equation $y = 8x$ is in the form of a proportional relationship.

Step3: Recall non - proportional relationship concept

A non - proportional relationship has the form $y=mx + b$ where $b
eq0$.

Step4: Analyze tech - repair problem

The equation for the mobile tech repair company is $y = 25.50x+50$. Since there is a fixed start amount ($b = 50$), it is a non - proportional relationship.

Answer:

1. B. $y = 8x$
2. B. Nonproportional; there is a fixed start amount.