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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