Question

Aunt Maggie’s car broke down on Interstate 10. Sam’s Towing charges a $57 hook up fee and $2.00 per mile towed. Regina’s Towing charges a $45 hook up fee and $2.50 per mile towed.

Select all statements that apply to this situation.

Question 5 options:

Both situations can be modeled using linear functions.


The y-intercept of the function that models Sam's Towing charges is 2.


The rate of change of the function that models Regina's towing charge is 2.5.


The y-intercept of the functions that model both situations represents the hook up fee.


The rate of change of the functions that model both situations represent the miles traveled per hour.

Answer 1

Both situations can be modeled using linear functions

The rate of change of the function that models Regina's towing charge is 2.5

The y-intercept of the functions that model both situations represents the hook up fee

Explanation:

Let

x -----> the number of miles towed

y ----> the total charge in dollars

we know that

The linear equation in slope intercept form is equal to

`y=mx+b`

where

m is the slope or unit rate of the linear equation

b is the y-intercept or initial value (value of y when the value of x is equal to zero)

we have

Sam’s Towing

In this case the slope of the linear equation is equal to the unit rate

The unit rate is $2.00 per mile towed

so

`m=\$2\ per\ mile\ towed`

The y-intercept is equal to the charge per fee

so

`b=\$57`

therefore

the linear equation is

`y=2x+57`

Regina’s Towing

In this case the slope of the linear equation is equal to the unit rate

The unit rate is $2.50 per mile towed

so

`m=\$2.50\ per\ mile\ towed`

The y-intercept is equal to the charge per fee

so

`b=\$45`

therefore

the linear equation is

`y=2.50x+45`

Verify each statement

case 1) Both situations can be modeled using linear functions

The statement is true

See the explanation

case 2) The y-intercept of the function that models Sam's Towing charges is 2

The statement is False

The y-intercept of the function that models Sam's Towing charges is $57

case 3) The rate of change of the function that models Regina's towing charge is 2.5

The statement is true

See the explanation

case 4) The y-intercept of the functions that model both situations represents the hook up fee

The statement is true

See the explanation

case 5) The rate of change of the functions that model both situations represent the miles traveled per hour

The statement is False

The rate of change of the functions that model both situations represent dollars by mile towed