Aunt Maggie’s car broke down on iterestate 10. Sams towing charges a $57 hoop up fee and $2.00 per mile towed. Reginas towing charge a $45 hook up fee and $2.50 per mile towed. Which of the following statements are true self all. Sketch the graph that represents the charges for Sam and reginas towing.

Answer:

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

Step-by-step 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

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

The y-intercept is equal to the charge per fee

so

therefore

the linear equation is

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

The y-intercept is equal to the charge per fee

so

therefore

the linear equation is

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

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